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KNOW YOUR OWN SHIP: 

A SIMPLE EXPLANATION 

OP 

THE STABILITY, TRIM, CONSTRUCTION, TONNAGE, AND 

FREEBOARD OF SHIPS, TOGETHER WITH A FULLY 

WORKED OUT SET OF THE USUAL SHIP 

CALCULA TIONS (FROM DRA WINGS). 

SPECIALLY ARRANGED FOR THE USE OF SHIPS' OFFICERS, 
SUPERINTENDENTS, ENGINEERS, DRAUGHTSMEN, 

AND OTHERS. 



BY 

THOMAS WALTON, 

LATE LECTURER ON NAVAL ARCHITECTURE TO SHIPS' OFFICERS AND STUDENTS 

IN THE GOVERNMENT NAVIGATION SCHOOL, LEITH, AND IN 

MIDDLESBROUGH SCIENCE SCHOOL; 

AUTHOR OF 

"CONSTRUCTION AND MAINTENANCE OP SHIPS BUILT OP STEEL. 



Witb IFlumetoud ^Uudttatfona. 



FOURTH EDITION. GREATLY ENLARGED. 



LONDON: 

CHARLES GRIFFIN AND COMPANY, LIMITED; 

EXETER STREET, STRAND. 

1899. 

[All nights Reserved,] 



/9\i 



■vrA 

, W2. 4- 



PREFACE TO FOURTH EDITION. 



During the three years which have elapsed since the First 
Edition of this work was issued, the Author has received 
numerous responses to the invitation then given for "sug- 
gestions and communications." These have come from ships' 
ofl&cers, engineers, and from students of naval architecture, 
working in shipyards. Though the original intention was to 
exclude the somewhat elaborate calculations involved in arriv- 
ing at many of the conclusions dealt with in this work — dis- 
placement, moment of inertia, righting moment of stability, 
etc., etc., — the communications received have proved beyond 
doubt that such calculations would be welcomed by a very 
large section of readers as a valuable addition to the book 
The author has been agreeably surprised to discover that 
many sea-going folk are not satisfied to merely understand 
and use the remits of calculations given to them, but are 
determined to know and understand the whole process of 
calculation^ by means of which these results are obtained, and, 
in consequence, very many hours have been spent in replying 
to queries of this nature. It will be evident that, as we come 
to deal with some of the more intricate calculations, a 
moderate amount of mathematical knowledge is required. 
However, it is hoped that by first dealing with the simple 
preliminary calculations in Chapter X., and then following on 
to the actual set of ship calculations, for which the necessary 
drawings are given, together with brief notes and explanations 



VI PREFACE. 

of the various steps taken, the reader will be able to trace the 
arithmetical application of the rules given. 

Considerable additions have been made in Chapter III. on 
the subject of water pressures, and in Chapter VI. (Section 
III.) on, the subject of* waterballast, to illustrate which 
numerous new diagrams have been inserted. Trim (Chapter 
VII.) is entirely new, and, it is hoped, will meet the require- 
ments of those readers at whose suggestions it has been intro- 
duced. This chapter, in the form of a paper, was read before 
the Shipmasters' Society in London, in March 1898, and the 
request was there repeated that it should find a place in 
Know Tour Own Ship. 

The other sections of the book have been revised, and, as far 
as possible, brought up to date. 

Suggestions involving details of ship construction will be 
fully dealt with in the companion volume, Construction 
and Maintenance of Steel Ships, undertaken by the Author 
at the special request of the publishers. - 

In its enlarged and improved form, it is hoped that this 
volume will meet with the same cordial acceptance which has 
been the chief characteristic of its history during its three 
years' existence. 

* Extracted largely from a paper read by the Author before the Ship- 
masters' Society, London, November, 1897. 

London, Aprils 1899. 



AUTHOR'S PREFACE TO THE 
FIRST EDITION. 



Experience is a wonderful teacher, though often a very slow 
one. In the course of time, it will instil into a seaman's 
mind a considerable knowledge of the capabilities and 
behaviour of his vessel under varying circumstances — her 
strength, her carrying capacity, her stability, or, in other 
words, her sea qualities. 

This mode of obtaining knowledge is, however, far too 
costly for the intelligent seaman of to-day. He knows that 
many a good ship, and what is worse, many precious lives 
have been lost before it has been acquired, and all through 
pure — though it would be unjust to say, wilful — ignorance. 

As regards the subject of stability, it has been said that it 
is useless to provide a captain with curves of stability, for he 
does not understand them, and if he did, they are of little 
use, all he requires being a statement of certain conditions of 
loading, beyond which he must not go, or his vessel will be 
unsafe. This is all very good in its way, but why does the 
captain not understand curves of stability, or, more broadly 
speaking, the subject of stability ? Is not the answer this, 
that very little indeed has been done to provide the means of 
his obtaining such important information? Besides, if the 
curves are of little use, and a statement of conditions to 



Vm PREFACE. 

ensure safety is sufficient, some credit must be given to the 
intelligence of the ship's officer of to-day. Let him not be 
put down as a machine to. steer a ship, incapable of compre- 
hending what may be reduced to a subject of comparative 
simplicity. On the other hand, let it not be supposed that 
lengthy experience in navigating ships necessarily means 
capability to so load any ship as to produce seaworthiness. 
The ignorance often displayed in loading and ballasting 
vessels, and the loss resulting therefrom, prove that such is 
not the case. 

It is evidently often imagined that able, valuable, and in- 
structive papers and lectures on vital subjects relating to 
ships, are only for, and interesting to, naval architects and 
experts, and that to ships' officers they are either unnecessary 
or else they have no' interest in this means of instruction. A 
more foolish and unjust conclusion could scarcely be arrived at. 
If the stability of a vessel depends so much upon the loading, 
and officers superintend the loading of their own vessels, at 
any rate in foreign ports, if not always at home, the importance 
of an intelligent knowledge of the subject must be evident. 

Moreover, is it not a fact that, with this knowledge, the 
ship's officer would be able to supply a great amount of 
valuable data to the shipbuilder and naval architect concern- 
ing the behaviour and capabilities of his vessel under every 
condition of weather and loading, which could not fail to be 
of immense value in the designing of future ships ? By this 
means, the designer, who, as a rule, sees little of the ship he 
designs after a few hours' trial trip, generally under the most 
favourable circumstances, would then be the better able to 
produce a vessel more perfectly adapted to her requirements. 

That such is the case is proved by the fact that some leading 
shipbuilding firms do everything in their power to encourage 



PREFACE. IX 

ship captains to give all the information they possibly can 
regarding the behaviour and performance of the vessels which 
they have built. 

The best method of supplying this kind of instruction to 
seamen is believed to be by means of lectures thoroughly 
illustrated by diagrams and experiments. 

During the past few years the writer has, in the Govern- 
ment Navigation School, Leith, N.B., given courses of 
lectures, specially designed for the instruction of seamen. 
The eagerness and enthusiasm displayed to obtain such in- 
formation made it manifest that seamen are fully awake to 
its importance, and appreciate and understand its value. The 
able discussion which often followed these lectures, and the 
important points and features brought out in connection with 
personal experience, furthermore proved that seamen want no 
rule-of-thumb methods for guidance, but that a thorough grasp 
of the principles of the subject is required. This, together 
with the repeated requests which have been made to publish 
these lectures, has tempted the writer to do so in the form of 
this book. The old-fashioned method of "beginning at the 
beginning " of the subject has been adopted as the only trust- 
worthy way of dealing with it; and while endeavouring to 
cover as much ground as possible, the aim has been to con- 
dense - the matter as far as compatible with clearness, to 
present it in language easy enough to be understood by every 
seaman, and stripped of laborious mathematical formulae, and 
at a cost which will place it within reach of seamen of limited 
means. 

It is felt that no apology is necessary in presenting this 
book, for while the excellent work of Sir E. J. Eeed and also 
that of Sir W. H. White are admirably adapted to the require- 
ments of the naval architect and the shipbuilder, it is beUeved 



X PRBFACB. 

that no special attempt has been made to supply the need of 
seamen generally. 

It is further hoped that the chapters on Construction, 
Tonnage, and Freeboard, while interesting and important 
subjects to seamen, will make the book acceptable to the ship- 
owner, ship superintendent, ship draughtsman, and to those 
generally interested in shipping. 

The Author's sincerest thanks are due to Messrs. W. Denny 
& Brothers, Dumbarton ; to Messrs. J. L. Thompson & Sons, 
Ltd., Sunderland ; and to Messrs. Eamage & Ferguson, Ltd., 
Leith, for permission to use curves of stability of vessels built 
by them; and also to J. Bolam, Esq., Head Master of the 
Government Navigation School, Leith, for the kindly sympathy 
and interest which he has manifested in the preparation of 
the book. 

Suggestions and communications — especially from ships' 
officers and others desirous of promoting this branch of 
nautical instruction — will be gladly welcomed and acknow- 
ledged in future editions of this work, should these be called 
for. 

Leith, March^ 1896. 



EDITOR'S PREFATORY NOTE 



This Series has been designed to meet the growing desire 
on the part of Ofl&cers in the Mercantile Marme for a 
MORE SCIENTIFIC INSIGHT into the principles of their pro- 
fession, and the sciences upon which the Art of Navigation 
is founded. The treatises are, for the most part, written 
BY Sailors for Sailors; and, where this is not the case, 
by authors who have special knowledge of the subjects 
dealt with and their application to the Sailor's life. The 
treatment will be thoroughly scientific, yet as free as pos- 
sible from abstruse technicalities, and the style such as will 
render it easy for the young sailor to gain a knowledge 
of the elements of his profession by private reading and 

without difficulty. 

KB. 

London, March, 1896. 



CONTENTS. 



Chapter I. — Displacement and Deadweight. 



PAQES 



Displacement — Displacement Carves — Deadweight — Deadweight 
Scale — **Tons per Inch Immersion" — Examples of Practical 
Application of "Tons per Inch Immersion" Curve — Coeffi- 
cients of Displacement, 1-11 



Chapter II. — Moments. 

Moments — Examples of Moments — Centre of Gravity — Effect 
upon Centre of Gravity of Moving Weights on a Ship, 
Vertically and Transversely, . * 12-18 



Chapter m. — Buoyancy. 

Buoyancy — Water Pressures — Reserve Buoyancy — Sheer — Value 
of Deck Erections — Centre of Buoyancy — Curves of Vertical 
and Longitudinal Centres of Buoyancy — Eflfect upon a Ship's 
Centre of Buoyancy of Immersing or Emerging Wedges of 
Buoyancy — Effect of Entry of Water upon Buoyancy — 
Camber, or Round of Beam — Testing Water Ballast Tanks, . 19-39 



Chapter IV. — Strain. 

Relation of Weight of Material in Structure to Strength — Strain 
when Floating Light in Dock — Relation between Weight and 
Buoyancy — Strain Increased or Decreased in Loading — 
Distribution and Arrangement of Material in Structure, so 
as to get Greatest Resistance to Bending — ^IVpes of Vessels 
subject to Greatest Strain — Strains among Waves — Panting 
Strains — Strains due to Propulsion by Steam and Wind — 
Strains from Deck Cargoes and Permanent Weights— Strains 
from Shipping Seas — Strains from Loading Cargoes Aground, . 40-60 



XIV CONTENTS. 



Chapter V.— Structure. 



PAaES 



Parts of Transverse Framing, and how Combined and United to 
produce Greatest Resistance to Alteration in Form — Sections 
of Material Used — Compensation for Dispensing with Hold 
Beams — Parts of Longitudinal Framing, how Combined and 
United to Transverse Framing to produce Greatest Resistance 
to all Kinds of Longitudinal Bending and Twisting — Forms of 
Keels and Centre Keelsons, and their Efficiency — Distribution 
of Material to Counteract Strain — ^Value of Efficiently-worked 
Shell and Deck Plating in Strengthening Ship Girder — Defini- 
tions of Important Terms — Illustration of Growth of Struc- 
tural Strength, with Increase of Dimensions, by means of 
Progressive Midship Sections — Special Strengthening in 
Machinery Space — Methods of Supporting Aft End of Shafts 
in Twin-Screw Steamers — Arrangements to prevent Panting 
— Special Strengthening for Deck Cargoes and Permanent 
Deck Weights, and also to Counteract Strains due to 
Propulsion by Wind — Types of Vessels — Comparison of 
Scantlings of a Three-decked, a Spar-decked, and an Awning- 
decked Vessel — Bulkheads — Rivets and Riveting, . . . 51-111 



Chapter VI. (Section I.).— Stability. 



Definition — The Righting Lever — The Metacentre — Righting 
Moment of Stability — Conditions of Equilibrium — "Stiff" 
and "Tender" — Metacentric Stability — Moment of Inertia 
— Agents in Design influencing Metacentric Height — How to 
obtain Stiffness — Changes in Metacentric Height during the 
Operation of Loading — Stability of Objects of Cylindrical 
Form — A Curve of Stability — Metacentric Curves — How the 
Ship's Officer can Determine the Metacentric Height and 
then the Position of the Centre of Gravity in any Condition 
of Loading — Effect of Beam, Freeboard, Height of Centre of 
Gravity above Top of Keel, and Metacentric Height upon 
Stability — Wedges of Immersion and Emersion — Effect of 
Tumble Home upon Stability — Stability in Different Types 
of Vessels, 112-147 



Chapter VI. (Section II.).— Rolling. 

Rolling in Still Water — Relation of Stiffness and Tenderness to 
Rapidity of Movements in Rolling — Resistances to Rolling — 
Danger of Great Stiffness — Rolling among Waves — Lines of 
Action of Buoyancy and Gravity — A Raft, a Cylinder, and 
a Ship among Waves — Synchronism : how Produced and 
Destroyed — Effect of Loaaing upon Behaviour — Effect of 
Transverse Arrangement of Weights upon Rolling Motions — 
Alteration in Behaviour during a Voyage — The Metacentric 
Height — Fore and Aft Motions — Fore and Aft Arrangement 
of Weights, 148-165 



CONTENTS. XV 



Chapter VL (Section ni.).— BaUasting. 



PAGES 



Similar Metacentric Heights at Diflferent Draughts — Wind 
Pressure — Amount- and Arrangement of Ballast — ^Means to 
Prevent Shifting of Ballast — Water Ballast — ^Trimming Tanks 
— Inadaptability of Double Bottom Tanks alone to provide an 
Efficient Means of Ballasting — Considerations upon the Height 
of the Transverse Metacentre between the Light and Load 
Draughts, and Effect upon Stability in Ballast— Unmanage- 
ableness in Ballast — Minimum Draught in Ballast — Arrange- 
ment of Ballast, 166-185 



Chapter VI. (Section IV.) 
Loading — Homogeneous Cargoes. 

Alteration to Curve of Stability, owing to Change in Metacentric 

Height— StabUity of Self-Trimming Vessels— Turret— Trunk, 186-192 

Chapter VI. (Section V.). — Shifting Cargoes. 
Variations in Stability on a Voyage, 193-197 

Chapter VX (Section VX) 
Effect of Aidmission of Water into the Interior of a Ship. 

Admission through a Hole in the Skin into a Large Hold — Curves, 
showing Variation in Height of Metacentre with Increase of 
Draught — Buoyancy afforded by Cargo in Damaged Com- 
partment — Longitudinal Bulkheads — Entry of Water into 
Damaged Compartment betieath a Watertight Flat — Entry 
of Water into Damaged Compartment beneath a Watertight 
Flat — Value of Water Ports — Water on Deck — Entrance of 
Water through a Deck Opening — Entry of Water into an 
End Comjmrtment — Height of Bulkheads — Waterlogged 
Vessels, 198-212 

Chapter VX (Section Vn.) 
Sailing— Sail Area, etc., 213-218 

Chapter VI. (Section VHI.) 
Stability Information, 219-221 

Chapter VI. (Section IX.) 
Closing.Remarks on Stability, 222-225 



XVI 



CONTENTS. 



Chapter Vn. — Trim. 

Definition — Moment to Alter Trim — Change of Trim — Centre of 
Buoyancy of Successive Layers of Buoyancy at Successive 
Draughts — Longitudinal Metacentre — Longitudinal Metacentric 
Height — ^Moment to Alter Trim One Inch — Practical Examples 
showing how the Change of Trim is Ascertained, 

Chapter YUL —Tonnage. 

Importance to Shipowners from an Economical Point of View — 
Under-deck Tonnage — Gross Tonnage — Register Tonnage — 
Deductions for Register Tonnage — Importance of Propelling 
Deduction in Steamers — Deep Water Ballast Tanks — Deck 
Cargoes — Examples of Actual Ship Tonnages — Sailing Vessels 
— Suez Canal Tonnage — Yacht Tonnage, . . , • . 

Chapter IX. — Freeboard. 

Definition — Method of Computing Freeboard — Type of Vessel — 
Nature of Deductions, and Additions to Freeboard — Examples 
of Estimating Freeboard for Different Types of Vessels, . 

Table of Natural Sines and Cotangents, etc., 

Chapter X. (Section I.). — Calculations. 

Useful Tables and Rules — Calculation of Weight of Steel Plate — 
Stanchion — Hollow Stanchion — Gallons in Fresh Water Tank 
— Tons in Coal Bunker — Rectangular Barge's Displacement and 
"Tons per Inch" Immersion — Simpson's Three Rules and 
Graphic Explanations — Calculation of Area of Deck or Water- 
plane — **Tons per Inch" Immersion of Ship's Waterplane — 
Ship's Displacement — Centre of Gravity of a Waterplane, Longi- 
tudinally or Transversely — Centre of Buoyancy, Vertically and 
Longitudinally — Moment of Inertia — ^Transverse Metacentre 
above Centre of Buoyancy — Centre of Gravity — Longitudinal 
Metacentre above Centre of Buoyancy — Alteration of Trim — 
Area of Section and Volume and Centre of Gravity of Wedge 
of Immersion or Emersion — Centre of Effort, . . • . 



PAOSS 



226-238 



239-250 



251-267 
268-270 



271-300 



Chapter X. (Section IL). 
A Set of Ship Calculations as Worked from Actual Drawings. 

Displacement — Longitudinal Centre of Buoyancy — Vertical Centre 
of Buoyancy — Transverse Metacentre above Centre .of Buoy- 
ancy, showing two Methods of Arrangement — Tons per Inch 
Immersion — Wetted Surface and SheU Displacement — Longi- 
tudinal Metacentre above Centre of Buoyancy — Results of 
Calculations upon Curves— Stability Calculation, . . . 301-324 

Appendix A : Dynamic Stability and Oscillations among Waves, . 325-328 

Appendix B : Test Questions, 328-332 

Index, 333 



KJS^OW YOUE OWN SHIP. 



CHAPTER I. 
DISPLACEMENT AND DEADWEIGHT. 

Contents. — Displacement — Displacement Curves — Deadweight — Dead- 
weight Scale — **Tons per Inch Immersion" — Examples of Practical 
Application of **Tons per Inch Immersion" Curve — Coeificients of 
Displacement. 

Terms. — " Displacement," " Deadweight," and " Tonnage " are 
terms often heard and used by those associated with ships and 
shipping in some form or other, but not always definitely under- 
stood. Their simplicity, however, renders them easy of explana- 
tion, and we shall, at the outset, devote our attention briefly 
to the two former — Displacement and Deadweight. The last 
— Tonnage — being a subject of larger dimensions, though simple 
in its character — will be reserved for a later chapter. 

Displacement. — ^Any object floating in water displaces or 
dislodges a volume of water, and the weight of the displaced 
water is equal to the weight of the floating object. The prefix 
"dis " in the word "displacement" means ** away from." Thus, 
displacement reveals its own meaning — viz., that which is placed 
out of its usual condition. 

Displacement, in the technical sense in which it is applied to 
ships, or any other floating bodies, refers to the displacing of the 
water by the total or partial immersion of any object placed in 
it. The volume of water displaced may be measured in cubic 
feet or in tons, and the weight of water displaced is called the 
Displacement, 

This fact may be simply illustrated by supposing a tank to be 

A 



KNOW YOUR OWN SHIP. 



filled to the brim with water, and when in this condition let a 
box-shaped ship— 3 feet long, 2 feet broad, and 2 feet deep- 
be placed in it, sinking to a depth of 1 foot. It is evident that 
if the tank were full before the ship was placed in it, some of 
the water must have overflowed (fig. 1). 

Let a receiver be placed below the tank, with a reservoir 
3 feet long, 2 feet broad, and 1 foot deep (exactly the same 
dimensions as the immersed part of the ship), attached to the 
bottom. It would be found that immediately the overflow had 
ceased, the reservoir would be just filled as shown by the dotteri 
lines. This proves that the volume of water displaced is exac>iy 







J 

&.0 f 






"■^^ 


zr~'C'zz 


< 1 

1 


— — 


— — — — — _ 


Z.1 




— — — — — ^ — — — 



\ 



"1 



■bzstolts:- 






1 



Fig. 1. — Displacement. 

equal to the volume of the immersed portion of the ship. More- 
over, if the ship could be placed in one balance, and the dis- 
placed water in another, they would be found to exactly equal 
each other in weight. But supposing the ship were too large 
for any process of weighing to be adopted, the displacement 
could be ascertained by a very simple calculation. 

A cubic foot of sea water weighs 64 lbs., and 35 cubic feet of sea water 
weigh 1 ton. Multiply together the length, breadth, and draught of the 
ship, and we get cubic feet ; 3x2x1 = 6 cubic feet. Therefore, since 
1 cubic foot weighs 64 lbs., 6 cubic feet will equal 6 x 64 = 384 lbs. dis- 
})lacement, and this, while being the weight of water in the reservoir, is also 
the total weight of the ship in its present condition. 

Again, sui)posing an unknown weight be placed in the ship increasing 



DISPLACEMENT AND DEADWEIGHT. 3 

the draught to 1 foot 6 inches, or 1*5 feet, then 3x2x1 -5 = 9 cubic feet, 
9 X 64 = 676 lbs. total displacement. 

The displacement, when the ship was empty, was 384 lbs., therefore the 
weight added is 576 - 384 = 192 lbs. 

In dealing with floating objects not box-shaped, such as real 
ships, although the same method of computing the displacement 



.scAue or tons 

JOO ^00 SCO AOO 



500 fioo 




Fig. 2.— Displacement Cueve. 



cannot be adopted owing to the difference in form, yet the 
principle, that the weight of water displaced equals the total 
weight of the ship, remains the same. This important fact, as is 
evident, proves of immense value to shipbuilder and shipowner 
alike, for had the weight of a ship to be found by estimating 
the weight of every item in it — hull, engines, boilers, masts, etc. 
— separately, and adding them together, it will be seen how 



4 KNOW YOUR OWN SHIP. 

laborious the process, and how inaccurate the result, might 
possibly be. 

The length, breadth, and draught of a ship cannot be multi- 
plied together for displacement, but, by the application of a 
simple method known as Simpson's rules, the volume of the 
immersed portion of the ship can be ascertained, which, if con- 
sidered as water, and divided by 35, will give the displacement 
in tons. (See Chapter X. for Simpson's Rules and Calculations.) 

To make a separate calculation whenever the displacement 
is required at any particular draught would entail considerable 
labour and inconvenience. This is avoided by using what is 
termed a Displacement Curve, by means of which, in a moment, 
the displacement can be read off at any draught. It is con- 
structed in the following manner (fig. 2). 

Draw the vertical line A B, and upon it construct a scale at, 
say, J inch = l foot, indicating the draughts up to the load line, 
exactly as read upon the stem or stem of a vessel, inserting in 
each foot space twelve equal divisions for inches. From the top 
of the line A B draw the horizontal line A C. Divide this line 
into ^-inch spaces, each one representing 100 tons of displace- 
ment. Subdivide the spaces again into tenths, each of which 
will, therefore, represent 10 tons. Supposing our vessel be of 
box form, 100 feet long, 20 feet broad, and 10 feet draught, then 
by calculating the displacement at a series of draughts, say 2, 
4, 6, 8, and 10 feet respectively, we are in a position to find a 
number of points by means of which the displacement curve is 
constructed. 

The displacement at — 

2 feet draught = 100 x 20 x 2 = 4,000 cubic feet 

4^-114-2 tons. 
35 

4 feet draught = 100 x 20 x 4 = 8,000 cubic feet 

?i^0-228-5tons. 
35 

6 feet draught = 100 x 20 x 6 - 12,000 cubic feet 

lM2?=342-8 tons. 
35 

8 feet draught - 100 x 20 x 8 = 16,000 cubic feet 

1^^=457-1 tons. 
35 

10 feet draught = 100 x 20 xlO = 20,000 cubic feet 

' 20,000 



35 

To construct the curve proceed as follows : — 



=571 "4 tons. 



DiapLACBMHKT AND DEADWBlGHT. 5 




KNOW YOUR OWN SHIP. 

Through the 2, 4, 6, 8, and 10 feet draughts on the scale 
draw lines parallel to the line AC. The displacement at the 
2 feet waterline is found to be 114*2 tons. Through the point 
in the horizontal scale of tons representing this, drop a vertical 
line to the 2 feet waterline. The intersection of these lines 
gives the first point in the curve. Repeat the same operation 
for the other displacements at their respective waterlines. A 
line through the points of intersection gives the displacement 
curve. For a box-shaped vessel, it is a straight line as shown. 
Having this, the displacement can be read off at any inter- 
mediate waterline between the bottom of the keel and the load 
waterline. The displacement curve for an actual ship is con- 
structed in the same way. Fig. 3 is an illustration of such an 
one. 

The load waterline in this case is 14 feet above the bottom of 
the keel, which .indicates on the curve 1400 tons of displacement. 
The mean draught of the vessel in her light condition is 7 feet, 
which reads from the curve 550 tons displacement, leaving a 
carrying capacity or deadweight of (1400-550 = ) 850 tons. 
Let these terms be clearly understood. Tlie total weight of the 
ship in whatever condition and floating at any draught is equal to 
the displacement at that draught, Deadioeight is carrying power 
only^ over and above the actual weight of the ship and her 
equipment. It, therefore, comprises cargo and bunker coal. 
The deadweight of a ship floating at a particular draught is the 
difference between tJie displacements in the light condition, and at 
that draught. 

From the displacement curve an even simpler method of 
indicating displacement can be arranged, useful more especially 
to the officer of the cargo-carrying vessel. This is a Vertical 
Displacement Scale, and with it is usually combined a Deadweight 
Scale (see fig. 4). 

Column 2 is a scale of draughts exactly similar to the scale 
of draughts on the displacement curve. Column 1 is a scale 
indicating the displacements corresponding to the draughts, the 
readings of which are identical with the readings from the curve, 
since the one is constructed from the other. For example, strike 
a horizontal line AB from the displacement curve to the ver- 
tical scale at, say, 8 •feet draught. The reading from the curve 
gives 655 tons, which is the same on the vertical scale. 
. Column 3 is a deadweight scale. As already pointed out, 
deadweight is the difference between tbe displacement at any 
particular draught and the weight or the displacement of the 
vessel when light. In the above case the vessel floated light at 
a mean draught of 7 feet, which represents 550 tons on the 



DISPLACEMENT AND DEADWEIGHT. 7 

displacement scale, while tlie deadweight stands at nil. The 
difference between the displacements at light draught and at 1 
foot intervals above the light draught will equal the respective 
deadweights at these draughts. 

Column 4 represents the freeboard. More about this will be 
found in Chapter IX. Suffice it for the present to state that 
by freeboard is meant the distance from the top of the weather 
decks at midships to the waterline at which the vessel floats. 
It is, therefore, measured from the deck downwards. In the 
above case the minimum freeboard was fixed at 2 feet. 

Thus, by means of the vertical scale, a ship's officer can read 
at a glance the total displacement — the deadweight and the 
corresponding freeboard — at any particular draught. 

Tons per Inch Immersion. — Another very useful curve, 
closely related to the subject of displacement, may be constructed. 
This is known as the Tons per Inch Curve, By " tons per inch " 
is meant the number of tons necessary to be placed on board or to 
be taken out of a vessel, to effect an increase or decrease of 1 inch 
in the mean draught. Thus the term " tons per inch " really 
means displacement per inch. It is found by calculating the 
displacement for a foot of the depth at the particular draught at 
■which the vessel is floating, and dividing this by 12. The result 
is the increase or decrease of the displacement for 1 inch altera- 
tion in draught, or " tons per inch." 

The area of the waterline in square feet is first found, and 
reckoning this to be a foot deep, the square feet are at onco 
converted into cubic feet. These cubic feet divided by 35 give 
the number of tons per foot. Tons per foot divided by 12 give 
the required " tons per inch." 

The formula may be written thus : — 

Area of waterline _ Area of waterline _ <, ^^^^ .^^. „ 
35 X 12 "" 420 * ^* 

The "tons per inch" for the box vessel, for which the dis- 
placement curve (fig. 2) was constructed, w^ould be : — 

100 X 20 = 2000 square feet area of waterline. . 
2000 X 1 = 2000 cubic feet of displacement. 

?2?2=47 "tons per inch." 
420 ^ 

It will be observed that since a box vessel is unchanging in 
horizontal section from the bottom to the top, the "tons per 
inch" will be the same at any draught, thus rendering the 
construction of a curve unnecessary. This is not so in the case 
of an ordinary ship. The waterplanes, from the top of the keel 



8 



KNOW YOUR OWN SHIP, 



8CAl.eOPTONS 



to the load waterline, all varying in form, necessitate the con- 
struction of a curve for readiness and convenience, so that the 
" tons per inch " may be ascertained immediately for any draught. 
This curve is made in the same manner as the displacement 
curve. The " tons per inch *' at the 4, 8, 12, and 16 feet heights 
above the top of the keel are 8'4, 9*7, 10*36, and 10*6 respec- 
tively. Vertical lines are dropped from these positions on the 
"tons" scale to their respective waterlines, the intersections of 
which give the points necessary for the construction of the curve 
(fig. 5). Its shape is somewhat different from the displacement 
curve for this reason. With every increase of draught the 
displacement must increase, and especially in the region of the 

load waterline, where the vessel 
is fullest in all ordinarily de- 
signed vessels, thus tending to 
make the curve continue to 
spread. On the other hand, 
the "tons per inch" increases 
rapidly until the vicinity of the 
load waterline is reached, and 
then the sides of the vessel, 
in the case of ordinary cargo 
steamers, being somewhat per- 
pendicular, there is little varia- 
tion in the area of the water- 
planes, and here the " tons per 
inch" remains about the same, the 
curve contracting and bending 
to a vertical position, as shown 
in the illustration. As an ex- 
ample of how to read the " tons 
per inch " curve at, say, 6 feet 
6 inches draught, strike the 
horizontal line AB to the curve. At the point of intersection 
draw a vertical line to the scale of tons, and there is indicated 9*1 
" tons per inch." 

The use of a curve of " tons per inch" may be illustrated in a 
variety of ways. 

For example, suppose a vessel to be floating at a certain 
draught, at which the "tons per inch" is 15. On calling at a 
port a moderate quantity of cargo has to be discharged, the 
weight of which is not exactly known. After discharging, the 
mean draught is found to have decreased 4J inches, therefore 
the weight of the cargo discharged is 15 x 4J = 67 J tons. 
Again, supposing a steamer floating at her load waterline, where 




Fig. 5. — "Tons per Inch" Curve. 



DISPLACEMENT AND DEADWEIGHT. 9 

the " tons per inch " is 15, to consume 100 tons of coal on a 
voyage, the decrease in draught would be -— - = 6*6 inches 

ID 

approximately. Every seaman knows that on a vessel psissing 
from salt to fresh water, an increase occurs in the mean draught, 
and a decrease when passing from fresh to salt water. The 
reason for this is, that salt and fresh water differ in density, 
and thus present different supporting qualities to objects floating 
in them. To support 1 ton of weight requires a displacement of 
36 cubic feet of fresh water, while salt water, being denser and 
heavier, and more capable of affording support, will bear up a 
weight of 1 ton on a displacement of 35 cubic feet. 

Sometimes where the depth of entrance to a dock is limited, 
it is very necessary to know what change of draught will occur 
in passing from salt to fresh water, or vice versd. At the load 
draught this is marked on the ship's side by the Board of Trade, 
or one or other of the Registration Societies, if the vessel is 
classed. By the aid of the ** tons per inch " curve, we may 
ascertain the change in draught for ourselves. Suppose a vessel 
to be floating at a certain draught where the displacement is 
4,500 tons, and the " tons per inch " 20. Now, a cubic foot of 
sea water weighs 64 lbs., and a cubic foot of river water, which 
is chiefly fresh, about 63 lbs., the difference being -^j* Since 
the total weight of the ship remains the same, the total weight 
of water displaced must remain the same also, though as it 
becomes fresh water it increases in volume, because it is ^^^ 
lighter, measure for measure. As already stated, when floating 
in sea water, she displaces 4500 tons. Suppose her now to be 
floating in river water at the same waterline, her weight or 
displacement will be -^^ less. 

,V of 4500 = 70*3 tons* 

The "tons per inch'* was 20 tons in salt water, but it also 
will be ^ less. 

20 X — = 191 J ** tons per inch " in river water. 
64 

The change in draught will therefore be — 

70-3 -r 191i = 3-57 inches. 
* Fresh water may be taken at 62i lbs. per cubic foot. 



10 



KNOW YOUR OWN SHIP 



The formula may be shortened, and written thus — 



s 



pj of displacement -i- -;- ol " tous per inch" = increase in draught; 



therefore, 



4500 



63 x20 



= 3*57 inches. 



Coefficients of Displacement. — In comparing the displace- 
ment or underwater form of one vessel with another, it is not 
sufficient to say that one is long and the other short, one broad 
and the other narrow, or one deep and the other shallow. Nor 
is a numerically correct idea conveyed by saying that one is fine 
and the other full or bluff. A more comprehensive means must 
be adopted, and this is attained by coefficients. 

Suppose that out of a block of wood 6 feet long, 1|- feet broad, 
and 1 foot deep, the model of the underwater form of a vessel 









6 -O 

Fig. 6.— Model of Underwater Form. 



■H 



be cut out, as shown by fig. 6, the extreme dimensions of which 

are — length, 6 feet ; breadth, 1^ feet ; depth, 1 foot. 

Before the block was cut, it contained 6x1^x1=9 cubic 

feet. The extreme dimensions of the remaining part in the 

form of the model are still the same — 6 feet long, 1^ feet broad, 

1 foot deep — but much of the volume of the block has been cut 

away, as shown by the hatched lines, leaving, say, 6 cubic feet, 

6 2 
which is -— == -^ , or, as it is generally written, '66 of the whole 

block, and this is termed the coefficient^ or, in other words, the 



t 



DISPLACEMENT AND DEADWEIGHT. 11 



comparison of fineness. Thus the coeflBcient of fineness of any 
vessel is the fractional part (usually expressed in decimals) which 
the volume of the displacement bears to the circumscribed block. 

•8 would be a very full vessel. 

"7 to 75, an average cargo steamer. 

•65, a moderately tine cargo steamer, 

•6, a fine passenger steamer. 

•5, an exceedingly fine steamer, but an average for steam yachts. 

'4, a very fine steam yacht. 

By means of coefficients a comparison of the displacement or 
fineness between two or more vessels may be struck relatively to 
their circumscribing rectangular blocks. 

Vessels of the same extreme dimensions, and the same co- 
efficients of fineness, and, therefore, the same displacements, may 
vary considerably in form or design, which in turn may affect 
the speed. 

Knowing the extreme dimensions of a vessel, and the coefficient 
of fineness, the exact displacement can easily be arrived at. For 
example, take a vessel 100 feet long, 20 feet broad, and floating at 
8 feet draught, the coefficient of fineness being -6. 

The displacement would be — 

l£5Jli2jUjLJ„ 27^.2 tons. 



12 KNOW YOUR OWN SHIP. 



CHAPTER 11. 

MOMENTS. 

Contents. — Moments— Examples of Moments — Centre of Gravity — Effect 
upon Centre of Gravity of Moving Weights on a Ship, Vertically and 
Transversely. 

Moments. — Moment of a Force about a Point. — We may 
speak of a ship when inclined from the. upright position as having 
a moment tending to bring her to the upriglit position again. 
This is usually termed a righting moment. On the other hand, it 
might be found that when the vessel was inclined to a certain 
angle, she possessed no inclination to return to her original upright 
position, but continued to heel until she capsized. In this case, 
we may say she possesses an upsetting^ or capsizing moment. 

This important term " moment " is easily understood. Every- 
body knows the meaning of simple distances like inches and 
feet, and of simple weights like pounds and tons. We must 
accustom ourselves to quantities which are got by multiplying 
distances by weights. Thus, we may have to multiply 5 feet 
by 8 tons. The product is called 40 foot-tons. If we multiply 
5 feet by 8 pounds, the product is called 40 foot-2^otmds. If we 
multiply 5 inches by 8 tons, the product is called 40 inch-tons. 
Now weight is one kind of force, and other forces, such as 
pressures and resistances (say, wind or steam ' pressure and water 
resistance), are also conveniently measured in pounds or tons. 
And pounds or tons of any kind of force, such as pressure and 
resistance, may also be multiplied by inches or feet of distance, 
giving inch-tons, or foot-pounds, etc., as the case may be. 

Now the quantity called the Moment of a Force (the only 
kind of moment we want just now) is got by taking some weight 
or other force and multiplying it hj what may be conveniently 
called its leverage. This leverage is the perpendicular distance of 
the direction in which the force acts from some conveniently 
chosen point. The point often chosen for this purpose in a ship 
is the centre of gravity of the ship. For instance, 5 tons of wind 
pressure on sails multiplied by a leverage from the ship's centre 
of gravity of 30 feet would give a moment of force about that 
centre of gravity of 5 x 30 = 150 foot-tons. And a water pressure of 
1000 tons multiplied by a leverage from the same centre of gravity 



MOMENTS, 13 

of 3 inches would give a moment of force about that centre of 
gravity of 1000 x 3 = 3000 inch-tons. 

Simple illustrations of moments of force may be got from 
levers. 

Let AB (fig. 7) be a lever 5 feet long, supported at one 
end, A, as shown, and at the other having a weight of 4 tons 
suspended at right angles to the lever. In this condition there 
is a moment about A of 4x5 (weight multiplied by distance 
from centre of weight to point of support) = 20 foot-tons, tending 
to capsize, or break, or bend the lever at the point A, and the 
20 foot-tons in this case may be called a capsizing moment, 




Fig. 7. — ^Weight Acting on a Lever. 

or a bending moment. Let the lever be subdivided into foot 
intervals at the points C D E F. If the weight be now moved 
to the point F, which is 4 feet from A, the moment about A will 
be 4x4 = 16 foot-tons. In like manner, if moved 

To the point E, the moment about A will be 4 x 3 = 12 foot-tons. 
D, „ » 4x2=8 „ 

,, ^i ti i> 4x1 — 4 ,, 

„ A, „ „ 4x0=0,, 

The last, no foot- tons, as will be seen, is accounted for by the 
fact that the downward force of weight is acting in the same 
vertical line as the upward support, there being therefore no 
capsizing moment ; or, as we are speaking of a lever or bar, no 
breaking or bending moment. 

There is just another point bearing on moments which will 
also assist us in studying the structure and strains of ships. 
In most cases the leverage is the variable factor in influencing 
the amount of foot-tons, the weight remaining constant. It 
should now be noticed tiiat the moment is alivays greatest at the 
point of support, and when the loeight is removed farthest from it. 
Keeping the weight in the position shown at B, the tendency 
to fracture at. the point C will be considerably less since the 
leverage is less. The moment at this point is 4x4 = 16 foot- 



14r KNOW YOUR OWN SHIP. 

tons, and it will continue to diminish until, at the point B, it 
has vanished completely. 

But let us take another simple example illustrative of 
moments. Fig. 8 represents a lever supported at the point A, 
and with weights of 3 and 4 tons suspended at its extremities, 
at distances of 8 and 5 feet respectively from the point of 
support. First, what would be the tendency to fracture at the 
point A ? On the side towards B there would be a moment of 



£ 



Fig. 8. — Action of Weights on a Point of SuppopwT. 

3 X 8 = 24 foot-tons, and on the side towards C, 4 x 5 = 20 
foot-tons. 

But suppose it is asked, "Is there a capsizing moment, and, 
if so, how much ? " As we have already seen, there is a moment 
of 20 foot-tons on the side towards C and 24 foot-tons towards 
B, and since the moment towards B preponderates by 24-20 = 4 
foot- tons, the lever would therefore capsize towards that side. 

Centre of Gravity. — But suppose we wished to find the 
point to which the support must be moved in order that the 
moments might balance one another, the lever remaining in a 
state of equilibrium or rest. This would be done by dividing 
the difference of the two moments, which was found to be 4, by 
the total weight 3 -h 4 = 7, 4 divided by 7 = 4- foot, and moving 
the support this distance towards B, the side possessing the 
greater moment. Let us prove this. The support, according 
to our calculation, will now be 8-f = 7|- feet from B, and 
5 + 4 = S-f feet from C. 

Towards B the moment is now 3 x 7^ — 22f foot-tons. 
„ G „ 4 X 5f - 22f „ 

Being exactly equal to each other, the lever remains at rest. 
Now this halancing point or centre of moments is a very important 
point. For the point at which a body (acted on only by its own 
weight) will balance is called the centre of gravity of that body. 
And the point at which a system of bodies (acted on only by 
their own weight) will balance is called the centre of gravity of 



HOMEXTS. 15 

that sydem of bodies. An example of a system of bodies is a 
ship with or without cargo in her. And as such a body as a 
ship cannot be balanced experimentally so as to find the centre 
of gravity by trial, the calculation of the moments in question 
is employed upon the ship and the weights in her until their 
balancing point is found, and that balancing point is the centre 
of gravity of the ship and the load then in her, aud the whole 
weight of ship and cargo may be supposed to act vertically 
downwards through that point. 

For, proceeding further, in ^g, 9, A B is a lever, with a weight 
of 2 tons at a distance of 2 feet from the support, and a weight 
of 4 tons at a distance of 4 feet from the support, both on the 
same side, and, similarly, weights of 2 and 4 tons at 2 and 4 feet 
respectively on the other side of the support. Then the moments 
must be the same, and it is evident that the lever is supported 

A B 



B^ 



"S ^ 



3 i 

: 



Fio. 9. — Centee of Gravity. 

at the centre of gravity of the total weight. Let a weight of 
3 tons be now suspended from the extremity of the lever at li, 
and at a distance of 6 feet from the support, as shown by the 
dotted square. It is required to find the centre of gravity now. 
Since the moments preponderate towards B by 3x6 = 18 foot- 
tons, if this be divided by the sum of the weights, we shall get the 
distance the centre of gravity has moved, which is j-lsslj^ feet 
towards B. 

But suppose that instead of a weight being added, the 2 ton 
weight on the side towards B be removed. Let us find the centro 
of gravity now. The moment towards A will preponderate by 
2x2 = 4 foot-tons, and this, divided by the total weight, which 
is 2 + 4 + 4 = 1 0, will equal -^ = f foot = shift of centre of 
gravity towards A. 

The reader is advised to make himself thoroughly familiar 
with the principle of moments, as illustrated in this chapter, as 
this will be found to be absolutely essential in order to deal 
successfully with the following chapters. Whenever several 
weights are connected by any means, as shown in the foregoing 
examples, the combined system of weights acts directly through 



16 



KNOW YOUR OWN SHIP. 



one balancing point, and this is their Common Centre of Gravity. 
And, if this method of finding the common centre of gravity of 
a ship and its load be used, one first finds how far from stem or 
stem that centre of gravity lies, and how much it is shifted fore 
or aft by shifting weights fore and aft. And precisely the same 
sort of calculation may be used to find how far above the keel 
the same centre of gravity lies, and how much up and down it 
is shifted by shifting weights up and down in the ship. We 
have only in this case to measure our leverages vertically above 
and below the balancing point we are trying to find by assuming 
a point for its position, and multiply the weights by the vertical 
leverages to get the moments. We, therefore, now proceed to 
show how to apply these principles to actual ships. 

Effect of Moving Weights on a Ship's Centre of Gravity. 
— Suppose a vessel be floating with her centre of gravity at the 




Fig. 10.— Centre of Gravity of a Ship. 



point G (fig. 10). (It may be said here that the position of 
the centre of gravity of the ship when light could be supplied 
by the builder, and this would limit the duty of the shipmaster 
to finding the position of the centre of gravity with various 
kinds of loading. But as it is not customary with all ship- 
builders to do this, a simple experiment by which the shipmaster 
himself may find the centre of gravity will be given later on.) 
Her total displacement — that is, her weight — is 1000 tons. Let 
a weight of 30 tons, already on board, be raised from the hold 
and placed on the deck, at a distance of 20 feet from its former 
position, as shown. What effect will this have upon the centre 
of gravity ? Since the centre of gravity is in the centre of the 
total weight it is evident that, if a tceight he raised, the centre 
of gravity must travel in the direction of the mx)ved weight To 
find the exact distance the centre of gravity has moved, the 



MOMENTS. 17 

same rule is adopted as in the case of a vertical lever. Multiply 
tlie weight moved hj the distance it is moved, and divide the result 
by the total weight or displacement, 

1000 lUOO 

the distance the centre of gravity has been raised. 

Again, suppose the weight, instead of being placed on deck, 
had been taken out of the vessel altogether. In this case, 
multiply the loeight by its given distance from tlie centre of gravity 
of the shipf say, 10 feet, and divide by tlie total displacement after 
the weight is removed (1000 — 30 = 970 tons = displacement 
after weight is removed), 

s^^^Q » §22 - -3 foot, 

970 970 ' 

the distance the centre of gravity has been raised. 

Again, suppose, when the displacement is 1000 tons, a weight 
of 30 tons be placed on board 10 feet below the centre of gravity. 
Multiply the new weight by its distance from the centre of gravity^ 
and divide by the new displacement (1000 + 30 = 1030 tons = new 
total displacement). 

30_>^10 „ 300^ . -28 foot, 
1030 1030 ' 

the distance the centre of gravity has been lowered. 

Stakboard. 




/ 
Fig. 11.— Effect of Weight Moved Athwartships. 

Let us now notice the effect of a weight moved athwartships 

(fig- 11). 

B 



18 KNOW YOUR OWN SHIP. 

The centre of gravity is in the position shown at G, and the 
total displacement is 1000 tons. 

A weight of 20 tons already on board, on the centre of the 
upper deck, is moved 10 feet to starboard. The centre of gravity 
must move in the same direction, and in a line parallel to the 
line joining the centres of the weight in its original, and in its 
new position. To find the exact distance moved, rmiltiply the 
weight by the distance moved, and divide by the total displacement, 

_20j^l0 _ ^ ^ .2 foot. 
1000 1000 

(G G^), the distance the centre of gravity has travelled to 
starboard. 



BDOTAKCT. 



CHAPTER III. 

BUOYANCY. 

COKTESTB. — Buoyancy — Water Pressores — Beserve Buoyancy — Sheer — Valae 
of Deck Erections — Centre of Bnoyaney — Curves of Vertical and Longi- 
tudinal Centres of Buoyancy — Effect upon a Ship's Centre of Buoyancy 
of Imineraing or EmergiDR Wedges of Buovancy — Effect of Entry of 
Water uoon Buoyancy — Camber, ot Bouna of Beam — Testing Water 
Ballast I'aaks. 

Buoyancy,- — Buoyancy means floating power. Under what 
conditions will a vesBel float t Simply when its enclosed water- 
tight volume is greater than its total weight in tons multiplied by 
35, since it requires that 35 cubic feet of salt water bo displaced 
before suflicient support is obtained to bear up 1 ton of weight. 
If the enclosed watertight volume of the vessel in cubic feet is less 
than its total weight in tons multiplied by 35, it will be evident 
that the vessel will sink. This we have learned from the chapter 
on "Displacement." But it may be aeked, "Why does a vessel 
float 1" or "What is the nature of the application of the pressure 
which is obviously produced by the water itself in order to sustain 
an object of greater or less weight floating upon it?" This we 
shall endeavour to explain. 




FlO. 12, — iLmsTBATIKO Wateh Suppokt, 



"Water Pressure. — Fig, 12 represents a tank nearly full of 
fresh water. At the left-hand end of this tank is a hollow 



20 KNOW YOUR OWN SHIP. 

cylinder made of, say, sheet iron. It is completely watertight, 
being entirely closed at the ends, one of which is a water- 
tight lid. By ordinary calculation, its volume is found to be 1 
cubic foot, the area of one end being 1 square foot and the height 
1 foot. When totally empty, with the ends closed, its weight is, 
say, 12 J lbs. A flat piece of sheet iron, similar to that from 
which this cylinder is made, would sink if thrown into the tank, 
while the sheet iron cylinder shows no signs whatever of sinking, 
but floats as shown, with more than three-fourths of its volume out 
of water. In order to immerse this tank so that its uppermost 
surface is level with the water surface, there would require to be 
an application of considerable downward pressure, which pressure, 
if measured, would be found to be equal to a weight of 50 lbs. 
(See second position of cylinder.) 

Or, supposing that, instead of a downward pressure applied to 
the outside, a weight of 50 lbs. had been placed inside the 
cylinder, and the whole suspended on a spring balance, the total 
weight registered will be 12J + 50 = 62J lbs. Suspended in mid 
air, it is clear that the entire support is afforded by the spring 
balance. While thus suspended, let the cylinder be gradually 
lowered into the water in the tank. (See third position of 
cylinder.) Immediately the bottom of the ' cylinder enters the 
water, and the immersion increases, the spring balance registers a 
reduction in weight, and this reduction continues in exact propor- 
tion to the rate of immersion, until, by the time that the cylinder 
is half immersed, it registers 31 J tons, and finally, when the 
uppermost surface is flush with the water surface, the balance 
registers 0, and the cylinder is barely maintained at the water 
surface. The addition of the slightest weight would send the 
cylinder to the bottom. Such an experiment as this, proves that, 
while a floating object is subject to the same gravitation forces out 
of the water as in it, the downward pressure of its weight is 
balanced by an exactly equal upward pressure from the water 
itself. Now, these upward water pressures are of enormous 
importance to a floating ship, for not only, as we have seen, do 
they aftbrd the support which keeps her on the bosom of the 
ocean, but are the means whereby, when she is forcibly inclined 
to a greater or less degree from the upright, she is enabled to 
regain her normal position, though, under other conditions, these 
same pressures may be the agents tending to capsize her when so 
inclined. (The stability aspect of the subject is dealt with in 
Chapter VI.). The foregoing experiment also enables us to 
estimate the nature of the application of the upward water 
pressures, for the spring balance clearly indicated that the 
amount of this pressure varies directly as the depth. 



BUOYANCY. 



21 



Thus, taking a rectangular object floating in salt water, as 
shown in fig. 13, it can be similarly demonstrated that, for 
every square foot of area on the bottom of the box, there is an 



Surface 



Upwmrd buoyant 
presmure per 

Mtfumrm faot 








Fig. 13. — Illusteating Water Pressure increasing in Proportion 

TO Draught. 

upward pressure of 64 lbs. at 1 foot depth ; at 2 feet depth 
the pressure is twice 64 lbs., and so on, in proportion to the 
depth. An attempt has been made to illustrate this by drawing 
the lines indicating the water pressures 
denser as the depth increases. 

Our next step is to ascertain the direction 
of the application of these water pressures. 

Take a vessel similar to that shown in 
fig. 14, whose sides are perforated with 
a considerable number of small holes. The 
vessel is filled with water, and it is found 
that from every hole the water squirts out 
in a direction sqjuare to the surface of the 
vessel, as shown. 

Or take the same" vessel empty, and 
plunge it into the water. Here, again, the 
water is seen to squirt into the inside of the 
vessel in a direction perpendicular to the 
surface of the vessel. From these two illus- 
trations it is evident that water contained in 
a vessel, large or small, exerts its pressure 
upon every unit of area on the inside, in lines 
of action perpendicular to the surface. On 
the other hand, when it is immersed, the 
pressure on its immersed surface is also perpendicular to that surface. 

So far, both by observation and the foregoing experiments, we 
have arrived at the conclusion that a floating object, whether it 
be the cylinder or a log of wood, or a 20,000 ton ship, is sup- 
ported, or enabled to float by upward pressure given by the water 




Fig. 14.— Water 
Pressure. 



22 KNOW TOUB OWN SHIP. 

itself, and, moreover, that the water pressure is exerted in lines of 
force perpendicular to the surface immersed — longitudinally, trans- 
versely, obliquely, and verticaDy, as shown by the lines of water 
pressures in fig. 15, tending to crush in the sides, ends, and bottom, 
or to push the vessel out of the water. This is understood all the 
move clearly when it is remembered that, immediately any floating 
object is taken out of the water, the water rushes in on all sides. 




Fia. IS.— Showing Lines op Watee pBEasuRE, 

Volume Immerseci - buorancy. Volume above water level = reserve buoyancy. 

and, more quickly than can be seen, the cavity formerly occupied 
by the object is tilled, and the water is again at its uniform level. 
Thus, while a ship is floating, the water has still the inclination, 
if the phrase may be so used, to occupy the space filled by the 
immersed volume of the vessel. Why the water does not succeed 
in crushing in the esterior of the vessel wil! be dealt with in 
another chapter on " structure." Why it docs not succeed in 
thrusting the ship out of the water has already been explained by 
the fact that there is the downward pressure of the weightof the 
^ip itselt Thus a vessel will sink to a draught such that the 



BCOTASCT. 



23 



reight 



Bum of the upward preasores of buovancy eiactJy eqaal the n 
of the ship. To balance & ship weighing, say, 500O tons, in mia 
air, by means of sapports, such a^ pillars of iron, would be no easy 
matter, A ship is a large, bulky object, and with such an 
enormous weight, a rery careful estimate of the strength of the 
supports and their positions would have to be made in order to 
ensure the necessary couditiooa being fulfilled. But in water, the 
support and balance are perfect. There are eiactly 5000 tons of 
supporting pressurea from the water to exactly support the 5000 




tons weight of the ship, and the balance ia perfectly effected bj- the 
centre of the support (or the resultant of all tlie upward 
pressures), and the centre of the weight being exactly in the 
same vertical line, which condition is absolutely essential iu order to 
preserve an esact balance : or, in other words, the centre through 
which the resultant of the buoyancy pressures is exerted (B, tig. ID), 
which is found to occupy a position in the centre of the displace- 
ment or immersed volume, and the centre of gravity (G) mtist be in 
the some vertical line iu order to ensure a condition of e<juiiibriiim. 



24 KNOW TOUR OWN SHIP. 

The net result is that, in a ship floating at rest, whether upright or 
inclined, we have two equal opposing forces, exactly neutrsdising 
each other, and therefore producing no motion whatever. 

Figure 16 shows the same vessel, forcibly inclined, and, as 
a result, the lines of force of gravity and buoyancy are no longer 
exerted in direct opposition to each other, G being in exactly the 
same position in the ship, while B has moved into the centre of 
the immersed volume. A ship, or any floating object, on being 
launched, or by any means placed in water, immediately, by these 
natural laws, places herself in such a position as we have described ; 
indeed, she must do so before a condition of rest can be main- 
tained. Such a position is not necessarily the upright, considered 
either transversely or longitudinally, but, under certain cir- 
cumstances, due to form and the distribution of weight 
constituting the ship and cargo, may necessitate the vessel 
inclining to port or starboard, or trimming by the stem or the 
stern. While the total buoyancy pressures and weight of a 
floating ship are equal to each other, it must not be imagined 
that these buoyancy pressures measure the total pressure upon 
the immersed hull of a ship. 




Fig. 17.— Showing the Total Pressure on the Immersed Hull 

OF A Ship. 

Figure 17 shows a box vessel floating, partially immersed. 
The lines of water pressures are shown vertical on the bottom and 
horizontal on the sides and ends (perpendicular to immersed surface). 

The horizontal pressures afford no support whatever, simply 
tending to push the vessel in the direction of their thrust. This, 
however, is balanced by the opposing pressures on the opposite 
side. The vertical surfaces of floating objects are exposed only to 
horizontal, crushing pressures ; such surfaces only as are horizontal 
or oblique are exposed to buoyancy pressures. So that a ship's 
immersed surface endures all the upward pressures providing 
buoyancy, or floating power, equal in amount, therefore, to her 
own weight, and all the horizontal pressures in addition, which 
afford no buoyancy, but simply tend to crush in the sides and ends 
of the vessel. It is clear, then, that to estimate the amount of 
buoyancy or upward pressure by using the total area of immersed 
surface would be entirely wrong. It must be distinctly under- 



BUOYANCY. 25 

stood that only upward pressures, either vertical or oblique, afford 
support, all others producing only crushing strains upon the 
vessel's immersed exterior. 

Remembering that supporting pressures increase in proportion 
to the depth, a difficulty sometimes arises in understanding the 
nature of the pressures in wholly immersed objects. For it is 
reasoned that, if it be true that upward pressures increase with 
depth, how comes it that, as soon as a vessel becomes too heavy to 
remain supported at the surface of the water, it never finds a place 
of rest until it reaches the bottom? The answer is simple 
enough. It is quite true that, as the object descends in sinking, 
the pressure on the bottom surface increases in direct proportion 
to the depth, and remembering that water pressures are always 
perpendicular to the immersed surface, the pressures on the upper 
surface of the sinking object also increase in direct proportion to the 
depth. Thus, while it is perfectly true that, as the object sinks, it is 
enduring an increased pressure upon the whole of its external sur- 
face in direct proportion to the depth, the increased upward pressure 
is balanced by a proportionately increased downward pressure. 

Since the law is so strictly enforced that no vessel shall proceed 
to sea loaded beyond her load watermark, except under penalty, 
it is of the greatest importance that the responsible authorities 
should exercise the greatest care in taking the correct load 
draught in the case of a vessel which has loaded aground. For 
it not unfrequently happens that a vessel registers a less mean 
draught immediately after becoming afloat than she did when she 
was aground. After the attention already given to buoyant 
pressures, the reason for this may be readily surmised. Suppose 
we could take one of the cylinders shown in fig. 12, and place the 
bottom surface in close contact with the bottom of the tank, so 
that neither air nor water could possibly get beneath it, we 
should then find that, though water surrounds it on all sides, even 
to its top surface, no buoyancy pressures are experienced by the 
cylinder, and therefore it has not the least floating power, even 
though it is in its light condition, weighing only 12 J lbs. 

But, more than this, we know that the atmospheric pressure at 
the earth's surface is 15 lbs. per square inch. Hence, if neither 
water nor air is capable of getting under the bottom surface of 
the cylinder, not only is there no buoyant pressure, but there 
is an atmospheric pressure of 15 lbs. on every square inch of the 
upper outside surface of the cylinder, as well as 15 lbs. per square 
inch on the internal surface of the cylinder, assuming, naturally, 
that it is filled with air, and not a vacuum. There is, therefore, 
a pressure of 15 lbs. per square inch on the inside bottom surface 
of the cylinder. And as this bottom surface contains an area 



26 KNOW YOUR OWN SHIP. 

of 1 square foot, or 144 square inches, the total pressure is 

144x15 = 2160 lbs., or nearly a ton, and against this there is 

not the slightest upward pressure from the water. 

Suppose, however, that the bottom of the cylinder is only 

partially in close contact with the bottom of the tank, so that 

neither water nor air could intervene over an area of, say, 10 per 

90 
cent, of the bottom. The buoyancy pressure would now be -— • 

of 64 lbs. (supposing the water to be salt) = 57*6 lbs., while the 
atmospheric pressure is 144 x -— -. x 15 = 216 lbs. The buoyancy 

pressure is 57*6 lbs., and the atmospheric pressure 216 lbs. ; the 
difference, 158*4 lbs., represents the preponderating downward 
pressure, indicating that the cylinder will not float. 

It is true, these are theoretical illustrations, though, in some 
degree, somewhat similar conditions are found to exist in the case 
of actual ships. It will depend upon the nature of the bottom 
upon which the ship is lying, and the amount of the bottom 
surface in close contact with the bottom upon which she rests. 
This is the only explanation which can be given for such an 
occurrence as described at the beginning of this feature of buoyancy, 
Avhere a ship registers a less draught after floating than imme- 
diately before when she was aground. 

Reserve Buoyancy. — Let it be imagined that a vessel float- 
ing at the waterline where the "tons per inch" is, say, 12 tons, 
has an additional weight of 60 tons placed on board. The result 
will be that the weight of the vessel having increased 60 tons in 
excess of the buoyancy, she must become further immersed. But 
how far 1 Well, since we have observed that 1 ton of buoyancy 
equals 1 ton of displacement, she will therefore sink until she 

has displaced 60 tons more water, which is an increase of — -, or 

5 inches in the draught. 

If, on the other hand, 60 tons be taken out of the vessel, the 
buoyancy will now be 60 tons in excess of the displacement, the 
result being that the vessel will rise out of the water until the 
buoyancy is reduced by 60 tons, and the draught is decreased by 

-— , or 5 inches. 
12 

Thus, we have here one of the conditions of a vessel floating 

at rest in still water — namely, that the total toeight of the vessel 

equals the total weight of tlie toater displaced, or the buoyancy. 

The buoyancy of the immersed portion of the vessel represents 

that which is requisite to keep her afloat. The buoyancy of all 



BUOYANCY. 



27 



enclosed -watertight space above the waterline is therefore surplus 
buoyancy, or safety buoyancy, or, as it is more commonly termed, 
Reserve Buoyancy (see figs. 15, 16, and 18). 

Sheer.— It is not sufficient that a vessel have just enough 
buoyancy to keep her afloat, for if she had only this, every wave 
would submerge her. It is the surplus buoyancy that gives her 
rising power, and, as we shall see in Chapter VI., provides righting 
power when inclined. The great advantage of sheer (fig. 18), 



S^^^^v^o^^Sivca^t^caiK^^ 





S= Sheer. Volume above line X, Y= Reserve buoyancy obtained by sheer. 

Fig. 18. — Sheeb. 

which gives surplus buoyancy at the ends of a vessel, will now be 
evident, for every time the vessel pitches into the trough of a 
sea, she immediately displaces more water than her weight, and 
is, therefore, thrown up again. 

Value of Deck Erections. — The Board of Trade recognises 
this to such an extent as to recommend a certain amount of sheer, 
according to the type of the vessel. When this amount is ex- 
ceeded, a reduction in the freeboard is allowed, and when the 
sheer is less an addition is made to the freeboard (see chapter 
on " Freeboard "). The value of poops and forecastles, especially 
the latter, and particularly if efficiently closed at the ends, will 
now be clearly understood, since they all add to the buoyancy, 
and at those parts of the vessel where it is greatly needed. 
Though not to the same extent in efficiency, yet all bridges 
with watertight ends, and deck houses and hatches — in short, all 
enclosed watertight erections afford reserve buoyancy. 

Centre of Buoyancy. — Now, just as the Centre of Gravity 
of the weights ranged on a lever can be ascertained, as explained 
in the previous chapter, so the centre of action of the numerous 
forces of buoyancy may be found; and since the forces acting 
upon any body may always be supposed to act directly through 
the centre of action, the value of this point will be readily 
granted, especially when we come to deal more closely with 
the subject of Stability. 

However, instead of speaking of the centre of action of the 
forces of buoyancy, this point is, for brevity, termed the Centre 
of Buoyanaj* and, moreover, it is found that the centre of 
buoyancy is the centre of displacement. Thus, to find the centre 

♦ B in figa. 16 and 16. 



28 



KNOW TOUR OWN SHIP* 



of buoyancy it is simply necessary to calculate the centre of dis- 
placement, as the two names indicate exactly the same poinjb. 
The centre of buoyancy being the centre of the displacement, it 
must vary in position with every variation of draught, so that it 
becomes necessary to arrange a convenient method of readily 
ascertaining the centre of buoyancy at any draught. This is done 
by calculating the centres of buoyancy at several draughts 
parallel to the load waterline, and constructing curves. By means 
of a calculation of moments, using horizontal areas of waterplanes, 
instead of weights as in the case of the lever examples in the 
previous chapter, the positions of the vertical centres of buoyancy 
are found at the required draughts. In a similar manner the 
longitudinal centres of buoyancy at several draughts are calcu- 
lated, and by using vertical areas of transverse sections of dis- 
placement at regular intervals fore and aft instead of weights, the 
several longitudinal centres of buoyancy may be found. See 
Chapter X. for examples of calculations. 




C.B.= Centre of buoyancy. 

Fig. 19.— Centre of Buoyancy of Box-shaped Vessel. 

Curves of Vertical and Longitudinal Centres of Buoy- 
ancy. — Thus, to find the actual centre of buoyancy, it is 
necessary to construct two curves, one for the vertical centres of 
huoijancy, to give vertical position, and the other for the 
longitudinal centres of buoyancy, giving longitudinal position. 
The intersection of the two lines is the point required. 

These curves, at the expense of little time and trouble, can be 
Supplied to the ship's officer by the shipbuilder or naval architect. 

To construct curves for a box-shaped vessel would be un- 
necessary, as it is evident that the vertical centres of buoyancy 
must always be at half the draught (see fig. 19), and the 
longitudinal centres of buoyancy at the middle of the length if 
floating with the bottom parallel to the waterline. 

Thus, at 10 feet draught, the vertical centre of buoyancy 
is 5 feet down from the waterline, at 6 feet draught it is 3 feet 
down from the waterline, and so on. 







Si,HOiaH dO 3-|«9e 



30 KNOW TOUR OWN SHIP. 

Curve of Vertical Centres of Buoyancy. — The heights 
of the vertical centres of buoyancy used in the construction 
of the curve in fig. 20 are for a vessel about 200 feet long, and 
with a draught of 14 feet when fully loaded. Suppose the 
vertical centres of buoyancy at the 4, 8, 12, and 16 feet draughts 
are found to be 1-2, 2-9, 4*9, and 6*6 feet respectively below 
their respective waterlines. To construct the curve proceed as 
follows : — Draw the lines A B and A C at right angles to each 
other. Let A B represent a scale of heights and A C a scale of 
draughts. Through the 16 feet height in the scale A B draw a 
horizontal line as shown, and through the 16 feet draught in A C 
draw a vertical line intersecting the other at D. From the point 
D set down the distance of the centre of buoyancy below the 16 
feet waterline = 6'6 feet. Proceed in the same manner for the 12 
feet waterline. Through the 12 feet height draw a horizontal 
line, and through the 12 feet draught draw a vertical line inter- 
secting the other at E. From E set down the distance of the 
centre of buoyancy below the 12 feet waterline = 4*9 feet. In a 
similar manner the centres of . buoyancy at the 8 and 4 feet 
waterlines may be set off. Through these points draw the line 
X y, which is the curve of the vertical centres of buoyancy required. 
By means of it the height of the vertical centres of buoyancy 
above the bottom of the keel may be read off at any draught. 

It will be understood that the curve constructed for any 
particular vessel will be of little use for any other vessel unless 
of exactly the same form and proportion in the immersed portion 
of the hull. But for the sake of example, let the curve in 
fig. 20 be for a yacht with a rising keel and drawing 10 feet 
forward and 13 feet aft. This represents a mean draught of 

=11 feet 6 inches. At 11 feet 6 inches on the horizontal 

2 

scale of draughts, set up a vertical line until it intersects the 

curve of the centres of buoyancy. From this point draw a 

horizontal line until it meets the vertical scale of heights, and 

there we read 7 feet, which is the height of the vertical centre 

of buoyancy above the bottom of the keel. Had the vessel been 

an ordinary cargo one, floating on even keel, and drawing 11 feet 

6 inches fore and aft, the height of the centre of buoyancy would 

have been the same. As has already been stated, this point, 

taken by itself alone, is of little use to anyone. It is only when 

used in relation to other points, with which we shall deal, that it 

possesses importance. 

Curve of Longitudinal Centres of Buoyancy. — The 

longitudinal centres of buoyancy for the same vessel of which fig. 

20 is the curve of the vertical centres of buoyancy are found to bo 



BUOTANCT. SI 

98'7, 99'2, 99-8, and 100 feet from the afterside of the stem post 
at the 16, 12, 8, and 4 feet waterlinea respectively. 

The curve would be constructed in the following manner (fig. 
21):- 

Draw the vertical line A B, and upon it construct a scale of 
draughts. From E draw the homontal line B C, and upon it 
construct a scale of feet, long enough to include the greatest 
distance of the centre of buoyancy from the stem post, which in 
this case is 100 feet. 98-7 feet on the line B C gives the first 
point in the curve. At 12 teet dranght draw a horizontal line, 
and through the point iu the scale indicating 99"2 feet drop a 
vertical line. The point of intersection gives the second point in 

SCALE ■or FEET 



















■* 




]^ 






^ 














p 














in 












R 





























S 






+ 














2. 




/ 















FiQ, 21.— Curve of Lokojtcdisaii Cestees of Buoyakcy. 

the curve. Proceed in the same manner with the 8 and 4 feet 
waterlines, obtaining the points indicated by the large dots. 
Through these points draw the line x y, which is the eune of the 
longitudinal ce:itres of buoyancy. Supposing we are asked to read 
off the longitudinal centre of buoyancy at, say, 7 feet 6 inches 
draught, we draw the horizontal line from the 7 feet 6 inches 
height in the scale of draughts until it intersects the curve, and 
from this point we strike a vertical line to the scale of distances, 
and there is indicated 99'6 feet from the afterside of the stern 
post. From this curve we can see that since the vessel is 200 
feet long, the displacements of the fore and after bodies are 



32 



KNOW YOUR OWN SHIP. 



exactly equal at the 4 feet draught, as the vessel's centre of 
support (centre of buoyancy) is at the middle of the length. 
Then, as the draughts increase, we notice that the centre of 
buoyancy travels a little towards the stern, showing that the after 
body is slightly fuller than the fdre body, increasing in this respect 
up to the load waterline. Now, we have simply reduced our ship 
to a huge lever, balanced practically- at the centre when floating 
at 7 feet draught. Suppose in this condition the vessel weighs 
550 tons, this being her displacement. She is then to be addition* 
ally loaded in the following manner : — 

r»0 tons are placed 20 feet abaft of the longitudinal centre of buoyancy. 
30 ., .. 60 



20 
40 



ft 



ti 
if 



30 feet forward 
70 



f) 



It 
it 
if 



it 

a 
if 



if 
a 
fi 



What effect will this have] First of all, we know that the 
draught will be increased. This could be found before the weights 
are placed on board, by adding the weights together, and referring 
to the displacement scale in figs. 3 and 4. 

550 + 50 + 30 + 20 + 40 = 690 tons, which reads 8 feet 4 J inches 
mean draught. 

There may be another effect. If the moments of the weights 
preponderate ahead or astern of the centre of buoyancy, then the 
vessel will trim* by the head or the stern, as the case may be. 
Let us see — 



Moments on after side of Centre 
of Buoyancy. 

50 X 20 = 1000 foot-tons. 
30 X 60 = 1800 ,, 



Total, 2800 



fi 



Moments on fore side of Centre 
of Buoyancy. 

20 X 30 = 600 foot-tons. 
40 X 70 = 2800 „ 



Total, 3400 



II 



Then, since the moments preponderate on the fore side by 
3400 - 2800 = 600 foot tons, the vessel will trim by the stem. 

But suppose we now wish to know what weight must be placed 
at, say, 25 feet aft of the centre of buoyancy to bring the vessel 
again on even keel — that is, with the new load line parallel to 
the keel. This would be discovered by dividing the foot-tons in 
excess by the distance the new weight has to be placed from the 
original centre of buoyancy. The result will be the required 
weight — 

600 



25 



= 24 tons. 



* By ti'im is meant the difference between the draught at the stem, and 
the draught at the stern. 



BUOYANCY. 33 

' It will now be seen that the moments on each side of the centre 
of buoyancy are equal. 

Vessels passing from salt or sea water to fresh or river water 
increase in draught. The reason of this has already been 
explained. 

Effect of Wedges of Buoyancy on Ship's Centre of 
Buoyancy. — Another thing which may be observed is, that not 
only do some vessels change draught in passing from sea to river 
water, but that they also change trim. The reason of this will be 
evident when it is known that in some vessels the fore body is 
fuller, and has more displacement than the after body. There- 
fore, in increasing in draught, the longitudinal centre of buoyancy 
•will travel forward (since it must remain in the centre of displace- 
ment), and the fore end of the vessel, having more support, will 
sink less than the after end. Hence, the change of trim. 

In lecturing before ships' officers, the question has more than 
once been asked : Is it possible, with a vessel trimming by the 
stem and the centre of the disc on the load waterline, to place 
any more cargo on board and yet not submerge the disc, and, con- 
sequently, not increase the draught ? 

To such a question it is certainly possible to answer " yes," but 
such a vessel would be so exceptional in her design that the answer 
is practically " no." 

For on examination of the lines of ordinary vessels, it is 
generally found that the fore body is slightly fuller than the 
after body, but this fulness takes place usually on the lower lines. 
At the region of the load line, however, the greatest fulness is 
usually aft, so that, imagining the vessel to be floating first at 
the waterhne W L (fig. 22), and then by shifting weights forward 




i'lG, 22. — Wedges of Buoyancy. 



to float at A B, the wedge y would generally be of greater volume 
than X. 

We have already seen that before a vessel will float at rest at 
any waterline, the weight of displacement and the buoyancy must 
equal each other. If by any means the weight of displacement 
be increased, the vessel will increase in draught ; if by any means 
the buoyancy be increased, the vessel will rise out of the water, 
and the draught will be decreased. 





34 KNOW YOUB OWN SHIP. 

Thus it follows that if the fore wedge x be less in volume than' 
the aft wedge y, the draught would actually be slightly increased 
since the buoyancy is less. If x and y be equal, no change will 
take place in the draught, and only when x is greater than y would 
any reduction in the mean draught be observed. Such is not 
likely to occur except in ill-designed vessels, for the effect upon 
the speed by the production of great resistance would certainly 
outweigh the consideration of carrying a trifle more deadweight at 
such a cost. 

Again, suppose the vessel to be floating at the waterline A B, 
and weights to be then shifted aft, so that the waterline is now 
at W L. If the volume of the immersed wedge y is more than 
the emerged wedge x, the draught will be somewhat decreased, 
and if y be less than Xj an increase in draught would occur. We 
have observed that the vertical centre of buoyancy is the vertical 
centre of the displacement, and that with every transverse move- 
ment of the vessel (whether by means of external force in river or 
dock, or under the influence of wind or waves) there is. a corre- 
sponding movement of the centre of buoyancy into the new centre 
of displacement. We shall now see how this new position may be 
found, and in this again the study of moments (Chapter II.) comes 
to our assistance. 

Fig. 23 is a cylinder 10 feet in diameter, 20 feet long, and 
floating at 5 feet draught. The displacement in this condition 
would be J X 10^ x -7854 x 20 = 785*4 cubic feet. B is the centre 
of buoyancy when floating upright. Let the cylinder be inclined 
to an angle of 20°. Observe clearly what takes place. W L was 
the original waterline ; after the inclination the waterline is W' L', 
so that the wedge A, which was previously actual buoyancy, has 
come out of the water and become reserve buoyancy, and the 
wedge B, which was formerly reserve buoyancy, has become actual 
buoyancy. (Let g and k be the centres of buoyancy of each of 
the wedges.) This simply amounts to shifting the wedge of 
buoyancy, with g as its centre, to the position of the wedge, with 
k as its centre, a distance of about 6J feet. Let the wedge, with 
g as its centre, equal 87 cubic feet, and, as just stated, the distance 
from the centre of buoyancy of the emerged wedge to the centre 
of buoyancy of the immersed equal 6J feet As the volume of 
displacement must be the same, at whatever angle of inclination, 
it follows that the wedge, with k as its centre, will equal 87 cubic 
feet. Now the new centre of buoyancy of the whole figure must 
have travelled in the direction in which the actual buoyancy was 
shifted ; that is, to starboard of its original position in the figure 
— viz., to B^, and in a line parallel to the line joining g and k, the 
centres of the wedges. The exact distance may be found by 






BUOYANCY. 



3& 



multiplying the volume of the wedge of buoyancy moved, 87 cubic 
feety by the distance moved, 6^ feet, and dividing by the total 
volume of displacement ; or, in other words, the volum^e of buoy- 
ancy. 

^ ^ = 'J2 feet, centre of buoyancy moved to starboard. 

In coming to vessels of ship form, the principle of finding the 
shift of the centre of buoyancy is exactly the same, but there is 



I* 




(cylinder floating upright 




Star 



69) 



Cylinder inclined to 20% 






Wedges of immersion and emersion. 

FiQ. 23.— Wedges of Buoyancy in a Cylinder. 



a difference in the wedges. In one respect, however, the two 
wedges in any one ship do not differ, and that is, that the volume 
of the wedge of immersion is always equal to the volume of the 
wedge of emersion. In cylindrically-shaped vessels, whose water- 
line passes through the centre of the cylinder, revolving as they 
do on the centre of their diameter, not only are the wedges equal 
in volume, but identical in shape, any sections of the wedges all 
fore and aft being exactly similar. This is not so with vessels of 
ship form, for in these the wedges of immersion and emersion vary 



36 KNOW YOUB OWN SHIP. 

very considerably in form, especially towards the ends, and even 
more so still if the angle to which the vessel is inclined be 
great. 

A little thought or personal observation of the actual form of 
a ship's hull will make this the more clear. 

Thus, while it is a simple matter to find the centre of gravity 
of the wedges of immersion and emersion of a floating cylinder — 
whose waterline passes through the centre of the cylinder — it 
entails more work to find the corresponding points in an actual 
ship ; and, while involving a considerable amount of labour, is not 
a matter of serious difficulty. (See Chapter X. for samples of 
Calculations.) * 

Effect of Entry of Water upon Buoyancy. — There is still 
another aspect of the subject of Buoyancy which calls for some 
attention. Suppose, first of all, that by some means or other a 
quantity of water enter the hold of a vessel. What will be the 
effect ? This will all depend upon how the water entered. Let 
us imagine that the sea breaking over the bulwarks entered by 
means of some deck opening — hatchway, for instance — the outside 
shell plating of the vessel being intact and perfectly watertight. 
The result of water finding ingress in this way would exactly 
resemble the result of loading cargo, the water being deadweight 
at the rate of 35 cubic feet to 1 ton. Should water continue to 
enter the vessel, the draught w^ould gradually increase until, if it 
happened that the total weight of the vessel, cargo, and water in 
her were more than the maximum possible displacement, she would 
naturally sink. If, on the other hand, when the hold was filled, 
the total weight of the vessel and the water in her were less than 
the maximum possible displacement, she would remain afloat — 
that is, disregarding the effect such might have upon the stability 
of the vessel, and also taking it for granted that little change of 
trim took place ; for otherwise, should the water find ingress into 
a large hold towards the end of a vessel, this might result in her 
going down by the head or stern, as the case might be. But let 
us take an entirely diff'erent case. Supposing the outside plating 
in the way of some hold be damaged below the load waterline, the 
sea would consequently russh in. If the hold were empty, it would 
fill, unless prevented, up to the level of the outside sea level, with 
water. But this is diff'erent from the former case, where water 
was poured into the hold from above. There the water acted as 
deadweight, but not so in this example, as there is now free com- 
munication between the water in the hold and the sea outside. 
What has happened is this : The vessel has been robbed of the 
total buoyancy, both actual and reserve, of this compartment, evea 
though it be found that, after increasing in draught, she still 



BUOYANCY. 



37 



floats with considerable freeboard. The empty space from the 
water in the hold to the top of the hatchway, as stated, is no 
longer reserve buoyancy, and the vessel has lost the entire 
buoyancy of this compartment ; and if it happens that the total 
buoyancy of the other intact compartments of the vessel is greater 
than the total displacement, as it was before the structure was 
damaged, and before the water entered, the vessel will float. If, 
ou the contrary, the vessel possesses less remaining buoyancy 
than this, she will be entirely immersed, and will sink. This will 
perhaps be somewhat clearer if illustrated by a box vessel, as 
shown in &g, 24. The vessel is divided into three watertight 



1 

w 


A 


i-^— -"^-s.^ 


A 


L 


"■' 


B 


IIS^ 


B 





Fig. 24. — Effect on Bfoyancy of Entry of Watek into 

A Damaged Compaetment. 



compartments by two watertight bulkheads, and floats at the 
waterline, WL. The centre compartment is damaged, and its 
actual and reserve buoyancy entirely lost, the sea having free 
entrance. If the sum of the volumes of A A (the reserve 
buoyancy) and B B (parts of the original actual buoyancy) be at 
least equal to the original actual buoyancy — that is, to the whole 
of the volume below the original waterline — it is possible for the 
vessel to float ; if it be less, she will inevitably sink. 

The reader must bear in mind that the inflow of water into 
such a hold as this has added nothing whatever to the weight 
of the ship, althougli the draught has increased ; the weight, or 
the total displacement, remains exactly the same, but the entire 
empty space in the damaged hold is to be left out altogether, and 
ignored in reckoning upon the actual and reserve buoyancy. In 
increasing her draught, the vessel has simply taken from the 
reserve buoyancy in the other watertight and intact compart- 
ments a volume equal to the volume of that part of the damaged 
compartment which was previously below the waterline, and 
which was, therefore, previous to the accident, in use as actual 
buoyancy. 

Again, suppose this accident happened to the vessel when her 
hold was filled with cargo, say timber, for example. How does 
she stand now ? The water will flow into the hold, and occupy 
vfh&t space it can. This will naturally be very small indeed, since 



38 KNOW TOUR OWN SHIP. 

the hold is already practically full. As the water cannot possibly 
occupy the space taken up by the timber, it has to be content 
with what remains. Therefore, the volume below the original 
waterline of all the corners and crevices not occupied by the 
timber is lost actual buoyancy, and the vessel will sink until she 
has taken from the reserve buoyancy a volume equal to the 
volume of the space unoccupied by the timber, and below the 
original waterline, which, in most cases, would be comparatively 
little. 

Camber or Round of Beam. — Vessels classed at Lloyd's 
require that all weather or uppermost decks have a round upon 
them, or camber, of at least j inch to 1 foot of beam. Thus, a 
vessel of 40 feet beam will have a camber of J inch x 40 = 10 
inches, and will, therefore, be 10 inches deeper at the middle of 
the breadth at midships than at the sides. One important 
advantage to be gained by this is an addition to the reserve 
buoyancy, and, little as it may seem, its importance is so re- 
cognised, that, if the stipulated amount of camber be reduced, an 
increase of freeboard is demanded ; if the amount be exceeded, a 
reduction in the freeboard is allowed. (See chapter on "Free- 
board.") 

Testing Water Ballast Tanks. — All water ballast tanks 
should be tested, in order to ensure that all joints and connections 
of plates and angle bars and the caulking be thoroughly watertight. 
This is done by means of water pressure. An iron pipe of the 
required length is fitted vertically into the top of the tank which 
is about to be tested. Water is then pumped into the tank until 
it is forced out at the top of the pipe. To accomplish this, 
considerable pressure has to be applied, which is in direct 
proportion to the height of the pipe. 

Supposing the pipe to be 1 square inch in sectional area and 20 

feet long from the crown of the tank, at the moment the tank is 

just full there is no pressure whatever upon the crown, but as 

soon as the water overflows at the top of the pipe it is evident 

that there must be a pressure at the bottom of the pipe of 

20 X 62i 

't — ^ =8*6 lbs. (fresh water). The pressure upon the inside 

of the crown of the tank must also be 8*6 lbs. per square inch or 
20 X 62|= 1250 lbs. per square foot. 

Lloyd's requirements for the testing of tanks in vessels classed 
by them is as follows : — 

Double Bottoms. — To have a head of water at least equal to 
the extreme draught — that is, the pipe previously mentioned must 
extend to the height of the maximum load line. 



BUOTAXCY. 39 

Deep Tanks and Peak Tanks, — To have a head of water at least 
6 feet above the crown of the tank. 

Fore and After Peak Bulkheads without Peak Ballast Tanks, — 
These are required to be tested by filling the peaks with water to 
the height of the load line. Other Bulkheads and Decks may have 
their watertightness tested by playing a hose upon them with a 
good head of water. 



40 KNOW TOUR OWN SHIP, 



CHAPTER IV. 
STRAIN. 

Contents. — Relation of Weight of Material in Structure to Strength — 
Strain when Floating Light in Dock — Relation between Weight and 
Buoyancy — Strain Increased or Decreased in Loading— Distribution 
and Arrangement of Material in Structure so as to get Greatest 
Resistance to Bending — Types of Vessels Subject to Greatest Strain — 
Strains among Waves — Panting Strains — Strains due to Propulsion by 
Steam and Wind — Strains from Deck Cargoes and Permanent Weights — 
Strains from Shipping Seas — Strains from Loading Cargoes Aground. 

Relation of Weight of Material in Structure to Strength. — 
It would be rather absurd to commence the study of the struc- 
ture of ships — whether they be steamers, sailing ships, or yachts — 
before first having some knowledpje of the strains which, under 
varying circumstances, they would most probably have to bear. 
To build a ship capable of enduring, without damage to its 
structure, every possible strain which might be brought to bear 
upon it, however excessive, would necessitate the introduction of 
such an amount of heavy material into its structure as to render 
it greatly deficient in its carrying capacity. It does not even 
follow that the vessel with the heaviest material is necessarily 
the best, or even the strongest, ship, but rather the one with the 
lightest material so combined as to give the maximum strength 
and efficiency, and sufficient to cover the strains which in all 
likelihood, under reasonable circumstances, would have to be 
endured. This is the aim of all such classification societies as 
Lloyd's, Bureau Veritas, The British Corporation, etc. 

Ships are built on a combination of two systems of framing 
— viz., longitudinal and transverse. 

Longitudinal framing includes all those parts in the frame- 
work of a vessel which run in a fore and aft direction, whose 
function is to afford longitudinal strength. 

Transverse framing includes all those parts in the frame- 
work of a vessel ^hose function is to give transverse or athwart- 
ship strength. ^ 

As has been aftteady indicated, the strongest ship is only 
obtained when thesa two systems have been intelligently woven 
together, the strengt* of the one co-operating with the strength 
of the other — that is\ in relation to the work which they have 



STRAIN. 



41 



to do. When this is accomplished the whole is then covered by 
a skin in the form of a shell-plating and decks, and by this 
means the skeleton or framework of the ship is still further 
united and strengthened. 

Strain when Floating Light. — Looking at an ordinary cargo 
steamer floating in the dock in her light condition, and lying at 
rest at her moorings, one would almost imagine at first sight 
that she is perfectly free from strain. But on investigation 
this is found not to be so. As ha^ been previously shown, any 
object placed in w^ater, whether it be a ship or a log of wood, 
will sink until it has displaced a volume of water equal in 
weight to itself. Or, in other words, before the object will 
remain stationary, and at rest at any waterline, the downward 






Figs. 25 and 26. — Stkains on Vessel Floating Light. 

pressure of the weight of the object floating must be exactly 
balanced by an equal upward pressure of the water. 

Relation between Weight and Buoyancy. — Supposing the 
vessel shown in fig. 25 be 200 feet long, and classed at Lloyd's, 
ehe would require four watertight bulkheads, one at each end of 
the engine and boiler space, a collision bulkhead at the fore end, 
and another bulkhead at the aft end. The weight of the vessel 
light being, say, 500 tons, if placed in the water would displace 
a volume of water 500 tons in weight, and would thus remain 
stationary, say, at the waterline, W L. 

But suppose the vessel could be divided off into five separate 
parts at the four watertight bulkheads, and each part floated 
separately, as shown in the sketch (fig. 26). It will now 
be seen that the draughts vary for each part, and none of them 
float at the original waterline. A little observation will soon 
explain this. The total weight of all the parts is exactly the 
same, and therefore the total water displaced is the same ; but 



42 KNOW YOUR OWN SHIP. ' 

throughout the length of the vessel there is an unequal distribu- 
tion of weight and buoyancy. Thus, for example, referring to 
the sketch, parts 1 and 5 — the euds of the vessel — ^being very 
fine, and yet of considerable weight, which is increased by the 
poop and forecastle, in order that they may be balanced by the 
buoyancy they will have to sink to the draught as shown. In 
parts 2 and i we have the vessel rapidly increasing in internal 
capacity or fulness, and small in weight in comparison with the 
volume of the enclosed space, the result being that these parts 
float at a less draught than previously. In No. 3 we have the 
fullest part of the vessel with greatest floating power. But in 
this compartment is concentrated the weight of engines and 
boilers, which tends to increase the draught upon what it is in 
the combined ship. Thus we see that throughout the length 
there is a series of upward and downward vertical strains, as 
shown by the arrows, tending to alter the form of the vessel 
longitudinally. Note that these strains tend to alter the form of 
the vessel. This alibrds one consideration for the naval architect 
or shipbuilder, in constructing an efficient ship — viz., that 
there is sufficient strength to prevent any such alteration in 
form taking place, or even any sign of such sjbrain being endured. 

Strains in Loading, — Now it can easily be seen how these 
strains may be considerably increased when loading ; for 
instance, if in the case of a miscellaneous cargo the heavy 
weights be placed towards the ends of the vessel where the 
buoyancy is least, the tendency of the ends of the vessel to 
droop would be greatly aggravated. The endeavour should be 
to distribute the heavy weights of the cargo so as to produce a 
balancing effect between the forces of weight and buoyancy, and 
thus avoid great local excess. By this means it is possible to 
reduce the strain even from what it is in the light condition. 
In considering strains at sea, the evil of bad loading will be 
seen still more clearly. 

In addition to these vertical strains to which the vessel is 
subject while lying at rest, there are collapsing strains acting 
upon every portion of the immersed skin of the ship (see 
fig. 15, Chapter III.). For, be it remembered that the forces 
of buoyancy act in perpendicular lines to the immersed surfaca 
Thus, while there is an upward pressure tending to thrust the 
vessel out of the water, there are also horizontal and oblique 
forces tending to crush in the sides of the ship. 

It will be obvious that the greater the immersed girth of the 
vessel, the greater the strain. Thus, the strain is greatest at 
midships, and on each side of midships ; and towards the ends, as 
the vessel becomes finer, it gradually diminishes. Considerable 



STRAIN. 



43 



as strains in still water may be under certain circumstances, 
on investigating the strains experienced at sea we shall see how 
enormously they are increased. 

First, observe the strains endured by a ship in the condition 
shown in fig. 27. Here the vessel is supported at midships 
on the summit of a wave, the extremities being practically 
unsupported. The ships may now be compared to a hollow 
girder with weights ranged miscellaneously throughout its length, 





Figs. 27 and 28. — Stbains of Vessels on Waves and in Thougks. 



and supported only at the centre, the result being a severe 
hogging strain tending to make the ends droop. 

Distribution of Material to Resist Bending. — The question 
now arises, How should the material employed in the con- 
struction of the vessel be distributed so as to withstand this 
tendency to bend? 

In fig. 29, let A 6 be a bar of iron or steel 100 feet long, 
supported at the middle of its length, and with a weight of 
10 tons attached to each end. This would not be an exact 
illustration of a loaded vessel supported at midships upon a 
wave as in fig. 27, but it will form a fair approximation to the 
strains experienced by a vessel when in a light condition with 
large peak ballast tanks full, or it will show the evil of loading 
a vessel with the heaviest cargo at the ends, and will serve to 
illustrate the principle it is wished to make clear. Let the 
sectional area of the bar be the same throughout its length. 
The bending moment of each weight would be 10 x 50 = 500 
foot-tons, and the tendency of the bar would be to bend or 
break at the point of support since the strain is greatest at this 
point. The tendency to break at 10 feet on each side of the 
support would be 10x40 = 400 foot-tons, and at 20 feet from 



44 



KNOW YOUR OWN SHIP. 



the support 10x30 = 300 foot-tons, and so on, the tendency 
to break diminishing towards the ends as the leverage decreases. 



^^a 



4<- — So* — 







B 



@ 



Fig. 29.— Strain on a Bab Loaded at each End. 

The bending moment at any section from the centre to the end of 
the bar might be graphically illustrated in the following manner : — 



---^ ^-— I. ^ 




Fig. 30. — Distribution of Bending Moment. 

Let "W «=» weight hung at each end of bar. 

,, L = hair-length of bar (that is, length from centre to end of bar). 
,, M = maximum bending moment (which occurs at centre of bar). 

Make M equal weight multiplied by leverage — W x L -» 10 x 50 — 600 

foot- tons at the middle of the bar. 
Join W. 

Let M be set off to any arbitrary scale ; then by using the 
same scale the bending moment can be measured at any inter- 
mediate position between the support and the weight. In a 
similar manner the strains experienced by a vessel supported at 
the middle of her length upon a wave are greatest in the region 
of the half length amidships. The structural arrangements in- 
troduced, and the great value of such erections as long bridges 
over the middle of the length in alibrding strength to resist those 
bending strains, will be shown at a later stage. 

Now, supposing the bar in figs. 29 and 30 to be 4 square 
inches in sectional area, the question may be asked. Is it possible 
to arrange the material, preserving the same sectional area so as 
to get greater efl&ciency in resisting longitudinal bending % Let 
the bar be rolled out so as to make it 8 inches by \ inch in 
section (same sectional area as previously), the length remaining 



STRAIN. 45 

the same. It will easily be seen that if the bar (or plate, as it 
now is) be supported as before with the wide 8-inch side hori- 
zontal, and the weights attached to its extremities, that it 
possesses less resistance to bending than when the bar was square 
in section. 

But should the bar be supported with its wide 8-inch surface 
vertical, it will be found that its resistance to bending has been 
increased beyond what it was in the square section of the bar. 
Let us make a brief examination of this difference of resistance to 
bending with the same sectional area. 

Let fig. 31 represent the 8-inch by |-inch plate, placed with 




3 

Fio. SI.—Bbnding Resistance of Bar placed Vertically. 

the 8-inch side vertically, and let A B be the neutral axis. (The 
neutral axis is an imaginary line of no strain passing longitudinally 
through, say, the centre of depth of the plate. Since the plate is 
8 inches deep, it will be 4 inches from each edge.) Supposing a 
weight be attached to each end of the plate, observe what must 
take place before it can bend. On the upper edge there must be 
considerable expansion or elongation, and on the lower, contraction 
or compression. The wider the plate is made, the greater will be 
the resistance to tensile strain on the upper edge, and compressive 
strain on the lower. It will also be found that the nearer the 
neutral axis is approached, the less elongation and compression 
are required to result in the same amount of bending, and at the 
neutral axis there is neither elongation nor compression. 

Now, theory and experiment agree in showing that the stretch- 
ing and compressive stresses at the top and bottom edges are now 
(8 inches by J inch, wide side vertical) only one-fourth of what 
they were when the bar was square in shape (2 inches by 2 
inches), and only one-sixteenth of what they are when the bar is 
8 inches by J inch, but laid with its thin edge vertical (the for- 
mally stated law is that the resistance of the bar to this kind of 
stress varies directly with tlie square of the dejpth of tlie bar, 
and directly as its breadth). 

The resistance to bending, moreover, will be greatly increased 
if the vertical plate be turned into a girder by attaching a bulb 



46 



KNOW TOUR OWN SHIP. 




to its upper and lower edge, as shown by A in fig. 32, or by 
adding strengthening flanges to the upper and lower edges, where 
the tensile and compressive strains are greatest ; for example, see 

IITTX 

ABC D E F 

Fio. 32. — Bending Resistance of Girders. 

fig. 32, B, C, D, E, and F. (Stress, Strain, and Strength are dealt 
with much more exhaustively in the author's companion volume to 
Know your own Ship,) 

Tjrpes of Vessels subject to Greatest Strain. — The prin- 
ciples which apply to a plate or girder apply equally well to a ship, 
for, after all, a ship is simply a huge, hollow girder, and from the 
foregoing reasoning the following deductions may be made :— 

1st. That vessels of great length, and therefore subject to 
excessive bending moment among waves, require more longi- 
tudinal strength than short ones (not necessarily more trans- 
verse strength). • 

2nd. That long, shallow vessels possessing less resistance to 
tensile and compressive strains require additional longitudinal 
strength. 

3rd. That in all vessels more strength is required in the 
region of midships, while a reduction may be gradually effected 
towards the ends. 

Strains among Waves. — In studying the case of a ship in 
the condition shown by fig. 28, it is observed that since the 
ends are supported on waves, and the midship part, containing 
engines, boilers, bunkers, etc., is to a large extent unsupported, 
the vessel, especially if a long one, will endure a severe sagging 
strain tending to make her droop amidships. There are cases 
on record where long, shallow vessels have actually fractured 
through the middle and sunk. The vessel may now be com- 
pared in some measure to a bar, supported at the ends with a 
weight in the centre, thus — 



—jp: 



SOL^^A 




Fig. 33.— Bak Weighted ik the Centre. 



STRAIN. 



47 



and if the weight be, say, 10 tons, and its distance from each 
support 50 feet^ then by the following diagram the bending 
moment may be illustrated : — 




Fio. 34. — Distribution of Bending Moment in Bab. 

Here, 10 tons in the middle gives 5 tons pressing on each 
support, and the bending moment in the middle ( =» pressure x 
leverage) = 5 tons x 50 feet = 250 foot-tons = M. 

Set off M (250) to any scale, and join CB and CA. By 
using the same scale, the bending moments can be measured at 
any intermediate position between the support and the weight. 
Here again in this illustration it is shown that the longitudinal 
bending moment is greatest at the middle of the bar correspond- 
ing to the midship portion of the ship, decreasing towards the 
ends, where it vanishes altogether. This provides another reason 
why vessels should have greater longitudinal strength amidships 
than elsewhere. 

Moreover, owing to the rapid transit of the waves, and, there- 
fore, the unequal distribution of weight and buoyancy, the 







Fig. 35.— Strains due to Rolling among Waves. 

vessel is subject to a succession of severe and sudden strains. 
It will also be seen that in rolling among waves, there is a great 
tendency for a vessel to alter in transverse form. Under such 
circumstances, she may be compared to a box, as shown in fig. 35. 



48 KNOW TOTTR OWN SHIP. 

If a series of irregular, collapsing strains be put upon the exterior 
of the box, the tendency is not so much to fracture in the positions 
shown by the wavy lines, but to work at the corners. Exactly 
the same thing takes place with a ship at sea as she rolls among 
the waves. The strain tends to have the effect shown in B, fig. 
35. 

Thus in determining the size and arrangement of all material in 
the construction of ships, there must be sufl&cient longitudinal 
strength to resist all longitudinal, bending forces, and sufficient 
transverse strength to resist all collapsing forces or alteration to 
transverse form of the nature already described, with a reasonable 
margin for safety. 

As has been already shown, it is not necessary to have as much 
sectional area of material towards the ends of the vessel as near 
amidships, since the strain is less ; but, nevertheless, in com- 
parison with the strain which has to be borne, both sections 
should be equally able to withstand such strains as come upon 
them, for it should be remembered that the vessel is no stronger 
than her weakest part. 

Thus far, only strains affecting the ship as a whole have been 
considered, but there are several other strains it is necessary to 
take into account which only affect the vessel locally. 

1. Panting Strains, — The fore end of the vessel, especially when 
of a bluff form of stem and driven at a high speed, being the first 
part to pass through the water, naturally suffers great head 
resistance, tending to make this part pant or work in and out. 

2. Strains due to Propulsion by Steam, — These strains may be 
divided into (1) strains owing to weight of engines and boilers, 
and (2) strains due to vibration of shaft, etc. 

3. Strains dice to Propulsion by Sail, — In vessels with lofty 
masts and much sail area, great strain is transmitted^ to the hull 
through the masts by the force of the wind and the action of 
rolling. 

4. Strains owing to lieavy j^^rmanent weights carried, such as 
winches, windlass, cranes, anchors, guns, etc. 

5. Strains from Deck Cargoes, — It is customary with many 
vessels, such as those engaged in the " Baltic " trades, to carry 
coal or some other British export on the outward voyage, and to 
return with cargoes of timber, and in order to get the vessel down 
to her load waterline large deck cargoes are carried. Many of the 
shipmasters engaged in such trades are not unacquainted with the 
fact that, owing to the heavy deck weight, these vessels ai'e 
severely strained, and sometimes take a set or sort of twist, and 
this is only discovered after the cargo has been removed, and 
perhaps not until even a few days later still, when the vessel, 



STRAIN. 49 

sometimes with a considerable report, frees herself from her 
strained condition with a severe trembling from stem to stern. 
On examination it is found that very many of the rivets in the 
heads of the hold stanchions or pillars have been sheared, and 
considerable damage done to the beam knees. This is an 
abundant proof that vessels intended to carry heavy deck cargoes 
require special strengthening. 

Such damage as that just explained might often be obviated by 
wedging or shoring the space between the top of the hold cargo 
and the beams, thus assisting the beams in enduring the strain 
of the deck cargo. 

* 6. Strains from the shipping of seas against poop or bridge 
fronts. Bridge and poop fronts with closed ends are subject to 
sudden and severe strains owing to the shipping of heavy seas, 
which will evidently spend their force against these bulkheads. 
Such parts, therefore, require special attention, and it is only 
possible to secure the maximum allowance on the freeboard when 
these parts are most efficiently constructed. 

7. Strains from Loading Cargoes Aground, — Vessels engaged 
in trades where it is known that they will lie aground during the 
operation of loading and unloading, require special stiffening on 
the bottom. And so on, cases might be enumerated where, 
special strain having to be endured, special strengthening must 
be provided. 

Excessive strains, such as those borne by a vessel when run 
ashore, as frequently happens, so that one end only is water-borne, 
or where the vessel, possibly laden with a heavy cargo, is laid 
across a sandbank, with ends unsupported when the tide has left 

* Strains from the shipping of heavy seas on deck are often more severe 
than is generally supposed, as shown by the following illustration. A fine 
new steel steamer, of nearly 4000 tons gross tonnage, was crossing the Atlantic 
in bad weather, in the beginning of the year 1899, when she shipped a heavy 
sea over the port side just in front of the bridge. The water fell with terrific 
force upon the fore main hatch and the deck. The hatch coamings on the 
port side were burst away, and the sea poured down into the fore main hold, 
damaging a considerable amount of cargo. Beams and stanchions were sprung 
and bent, the rivets in the beam knees sheared, and the deck considerably 
damaged. The sea, in sweeping over the starboard side, carried nearly the 
whole of the bulwarks with it. All this damage was caused by the shipping 
of a single sea, for the vessel shipped very little water afterwards, which gave 
the crew an opportunity of temporarily closing up the damaged hatchway. 
The vessel was comparatively new, being built to Lloyd's highest class in 1898, 
yet it seems quite certain that if she had shipped another sea of a like nature, 
she would have foundered, and contributed to swell the list of vessels 
"unheard of" or "missing." Too much attention cannot be paid to the 
thorough protection of all deck openings, both hatchways and engine casings, 
for it is very probable that the loss of most of those vessels which are never 
again heard of is caused by accidents of a similar nature to that just described. 



50 KNOW YOUR OWN SHIP. 

her, the shipbuilder cannot attempt to cover, but all strains, such 
as those already mentioned, may be thoroughly provided against. 

A vessel in dry dock, unless carefully shored, may be consider- 
ably damaged. Cases of dry docking, where the bilges have 
drooped, have occurred through carelessness or ignorance. Having 
briefly enumerated the chief strains borne by a vessel under 
various circumstances, the reader will now be better prepared to 
understand why exceptional strength is introduced into the 
structure, either considered as a whole, or in particular parts only. 



STBUCTUBH. 51 



CHAPTER V. 

STRUCTURE. 

Contents. — Parts of Transverse Framing, and How Combined and United 
to Produce Greatest Pesistance to Alteration in Form — Sections of 
Material Used — Compensation for Dispensing with Hold Beams — Parts 
of Longitudinal Framing, How Combined and United to Transverse 
Framing to Produce Greatest Resistance to all Kinds of Longitudinal 
Bending and Twisting— Forms of Keels and Centre Keelsons, and their 
Efficiency — Distribution of Material to Counteract Strain — Value of 
Efficiently-Worked Shell and Deck Plating in Strengthening Ship 
Girder — Definitions of Important Terms — Illustration of Growth of 
Structural Strength, with Increase of Dimensions by means of Pro- 
gressive Midship Sections — Special Strengthening in Machinery Space 
— Methods of Supporting Aft End of Shafts in Twin- Screw Steamers — 
Arrangements to Prevent Panting — Special Strengthening for Deck 
Cargoes and Permanent Deck Weights, and also to Counteract Strains 
due to Propulsion by wind — Types of Vessels — Comparison of Scant- 
lings of a Three- Decked, a Spar- Decked, and an Awning-Decked Vessel 
— Bulkheads — Rivets and Riveting. 

Transverse Framing. — The parts of the structure of a ship 
affording resistance to transverse strains, according to the usual 
mode of construction, are included in the combination known as 
transverse framing, A complete transverse frame comprises a 
Jrame bar, a reverse bar, a floor ;plate, a beam, and a jjillar, 



BOSOM PIECE. 



BBHB 



Section showing angle bar fitted to bosom 
of frame and coveiing butt. 



/BUTT 



\ <^ BOSOM }^ PIECE » y 



PLAN. 

Fig. 37. — Angle Bar. 

efficiently united. According to the size of the vessel, the 

spacing of the transverse frames varies from about 20 to 26 * 

inches from stem to stem. Let us take for our example an 

ordinary merchant steamer, a midship section of which is shown 

in fig. 36. 

• A leading Liverpool Shipping Company is adopting a System of spacing 
the Transverse frames 36 inches apart. 



52 



KNOW YOUR OWN SHIP. 



SHELU 
PUATINQ 




^ 



FRAMC 



B 




FRAME 



i^REVERSE 
FRAM& 



The frame har extends continuously from keel to gunwale in 

this type of vessel. Should there, 
from any cause, be a break in the 
length of the frame, the strength 
should be preserved by lapping the 
parts to make the connection, or by 
fitting angle butt straps, or other 
efficient means of compensation should 
be adopted (see fig. 37, and section 
AB in fig. 36). This, indeed, is a 
rule which should be rigorously ob- 
served throughout the construction 
of a ship, that wlierever a structural 
part is weakened, the strength he fully 
recovered hy compensation in some form 
or other. If the frames meet or butt 
on the keel, as they usually do, they 
are connected by pieces of angle bar 
about 3 feet long, fitted back to back, 
which, in addition, provide a sub- 
stantial means of connection to the 
shell plating. The usual form of 
frame is the plain angle bar (see A, 
fig. 38^. 

It will be noticed that one flange 
of the bar is longer than the other ; 
the long flange always points into 
the interior of the ship, and the 
short one is attached to the shell 
plating. Since the greater the girth 
of the vessel, and thus the greater 
the collapsing strain, it is evident 
that the vessel needs more transverse 
strength in the region of midships, 
where it is fullest, than towards the 
ends. It is, therefore, usual to make 
the frames one-twentieth of an inch 
thicker for three-fifths of the length 
at amidships than at the ends. The 
frame bar is made stronger and more 
rigid, and, therefore, the better able 
to keep out the ship's side by means 
of a reverse har, which is similar in 
section, but smaller in size. It is 
riveted to the back of the frame (see B, ^g, 38), and being 




n 




Fig. 38.— Fbame Bars. 



STRUCTURE. 53 

on the side of the frame hidden from view in fig. 36, it 
is there shown in dotted lines. The reverse bar does not 
always extend to the same height as the frame. As will be 
seen further on, its height is governed by the tmnsverse dimen- 
sions of the vessel, for the greater the girth and beam, the 
greater the need for transverse strength. Across the bottom 
of the ship, and extending well up the bilge, is a deep plate 
called a floor plate. On the lower edge of this plate is attached 
the large flange of the frame bar, and across the other side on 
the upper edge is bent and riveted the reverse angle after it 
leaves the frame (see section A B, ^g, 36). The floor plate, 
being now converted into a girder, affords great stiffness and 
strength to the bottom of the ship. 

Instead of the usual frame and reverse frame there are other 
sections of bar iron or steel which may be used. For example, 
there is the Z-bar (see C, fig. 38), which is a combination of 
the frame and reverse frame rolled in one section, thus saving 
the necessity of riveting these two together. It is very strong, 
and is extensively used in the building of ships for the Royal 
Navy. 

A very similar bar to this, sometimes used for framing large 
vessels, is the channel iron section shown in D (fig. 38). 

This also saves the riveting of a reverse bar. When this 
section is used, it is generally dispensed with towards the ends 
of the vessel, and the ordinary frame and reverse angle bar 
substituted, as it is difficult to bend and bevel the channel bars 
as required at the ends of the vessel. There is also the bulb 
angle section (see E, ^g. 38). 

This is sometimes adopted in vessels where no sparring is 
required in the holds, thus permitting some kinds of cargo to be 
trimmed right against the shell, an advantage being gained in 
cubic capacity. By this means also the reverse bar may be 
dispensed with when the bulb angle is made strong enough to 
equal the frame and reverse bars together. 

The beams form an important part of transverse framing, unit- 
ing, as they do, the upper extremities of the frame bars and 
holding them in position, thus forming the foundation for decks. 
In addition, they complete the transverse section of the hollow 
girder into which we have resolved our ship. It would be 
useless to secure sufficient structural strength in the various 
bars forming the transverse skeleton of a vessel, unless at the 
same time every attention were given to the efficient connection 
of these parts to one another. We have already noticed how 
the frame butts are strengthened and connected, but there is 
Btill the connection of the frame and the beams. This is done 



54 



KNOW YOUR OWN SHIP. 



by welding or riveting to each extremity of the beam a hiee 
2)laie (fig. 39), which is fitted into the bosom of the frame. 

The British Corporation 
recognises the necessity of an 
efficient connection at this 
part, by compelling all ships 
built under its survey to have 
knees three times the depth 
of the beam, and one-and- 
three-quarters the depth at 
the throat, to all beams in 
the way of the main deck. 
Lloyd's require the depth of 
the knee to be two-and-a-half 
times the depth of the beam, 
and one-and-a-half times the 
depth of the beam at the 
throat for steam vessels, while 
for sailing ships over 36 feet 
broad the knees must be 
three times the depth of the 
beam. 

Like frame bars, the beams 
may vary in sectional form. 
Under iron or steel decks it 
is usual and better to fit 
angle or angle bulb beams 
to every frame, and under 
wood decks, on alternate 
frames, beams of the following 
sections may be adopted: — 

(1) Butterly Bulb (see A, 
fig. 40). 

(2) Bulb Plate, and double 
angles riveted to its upper edge (see B, fig. 40). Or, 

(3) Channel Bar (see D, ^g, 38). 

B A 




Eleyatlon. 



^ 



FRAMe 



C: 



BEAM 



. 



Plan. 
Fig. 89.— Beam Knee. 





Fig. 40. — Beams. 



However, these forms may be considerably modified according 



STRUCTURB. 



55 



to the length of the beams, since the length of the beams 
determines the size of bar to be used. Vessels may have two, 
three, four, or more tiers of beams, according to their depth. 

Compensation for Dispensing with Hold Beams. — Now, 
let us suppose a shipowner is about to have a vessel built with a 
depth of 16 feet. He finds, if he intends to class the vessel at 




Fig. 41. —Substitutes for Hold Beams, 

Lloyd's, that she requires hold beams fastened to every tenth 
frame, and at the extremities of the beams a stringer plate (see 
^g, 36) securely attached to beams and shell. But as these 
would interfere with the stowage of cargo he intends to carry, 
let us see what alternative he may adopt in order to dispense 
with the hold beams. If he wishes, he may fit transverse web 



56 KNOW YOUR OWN SHIP. 

frames (see fig. 41) at distances of eight frame spaces apart all 
fore and aft ; this compensates for loss of beams. 

In addition, there must be fitted a longitudinal web frame, or 
web stringer as it is called, all fore and aft, between the trans- 
verse web frames, and securely attached to them by angles on 
the upper and the lower sides, and also by means of an efficient 
diamond plate on its front edge. This compensates for the loss 
of the stringer plate on hold beams. The next thing to be done 
is to have the upper extremities of the web frames firmly tied 
together and held in position. This is done by fitting extra 
strong beams across the vessel, attached to the web frames by 
extra strong deep knees. Since the function of the beam and 
stringer plate is to tie and stiiffen the sides of the ship, the web 
frame being a transverse plate girder, and the web stringer a 
longitudinal plate girder, the one firmly united to the other 
enables them to dp their work together, and thus serve the same 
purpose. It will be observed that the web frame shown in fig. 
41 is a continuation of the floor plate, and also that both it and 
the web stringer are stiffened by double angles on their inner 
edges. 

Another alternative is to stiffen the ship at every frame space 
all fore and aft by fitting together two large angles (as shown in 
fig. 55). In conjunction with special hold stringers, this method, 
known as "Deep Framing," makes a substitute for both hold 
beams and reverse frames. 

There is still another part in the transverse framing to be 
noticed — viz., the 'pillars. They are riveted to the beams, 
and usually to the girder on the top of the floors, or some other 
part of the bottom of the vessel. They bind the upper and lower 
parts of the structure together, and perform the function of a 
strut and a tie by holding the beams and the bottom of the ship 
in their right positions relatively to each other ; and thus by 
uniting the two great horizontal flanges of the ship girder, the 
deck and the bottom, they enable them to act in unison in 
resisting longitudinal strains. 

When considering the subject of strains, we noticed that in 
rolling among waves a vessel has the tendency to alter her 
transverse form, and to work at the comers. After observing 
the combination constituting transverse framing, we shall now 
be able to see how these parts unite in offering resistance to 
the alteration of transverse form, 

1. At the Bilge Corners. — Here we have the floor plate curved 
np the bilge to a height of twice its depth at the middle line of 
the vessel, thereby supporting the bilge in the form of a web at 
every frame. 



STBUCTUBB. 57 

2, At tlie Deck Corners, — In this case we see the efficiency 
developed by the deep beam knees in giving support in the form 
of webs at every beam. Fig. 55 shows a similar web in a double- 
bottomed vessel. 

3. Furthermore, there is the great assistance provided in the 
form of the beams themselves holding the sides of the vessel 
rigid, the beams being in their turn supported by the pillars. 

Longitudinal Framing. — The longitudinal framework of the 
vessel is made up of the keel^ keelsons^ and stringers. These may 
partake of a variety of forms, with a view of which we shall 
briefly deal, together with the means adopted for binding them 
all together in order to secure an efficient and strong framework. 
The number of keelsons and stringers depends upon the size and 
proportions of the vessel. 

Keel, — ^The keel shown in fig, 36 is known as the ordinary bar 
keel. It is made up of long lengths of bar iron connected by 
means of scarphs, the length of which should be sufficient to secure 
a good connection (see fig. 42). If the vessel be classed at Lloyd's, 



CLCVATION OF K £ S L. 




P LAN 

Fig. 42. — Keel. 

the scarphs will be nine times the thickness of the keel, and if 
with the British Corporation, three times the depth of keel. 

The same method of connection unites the keel to the stem 
and the stem posts. These connections may also be made by 
welding, but this is seldom done. 

A superior arrangement of this kind of keel is the one known 
as the side bar keel (see E, fig. 43). 

It consists of a deep plate extending down from above the top 
of the floors to the bottom of the keel, the thickness of the keel 
part being made up by attaching two side bars or slabs of iron, 
one on each side of the lower extremity of the centre plate. 
The whole is then riveted to the two strakes of shell plating 
which cover the keel, and are called the garhoard strakes (see 
fig. 36). A thoroughly strong result is thus secured. Holes 



58 



KNOW TOUR OWN SHIP. 



are cut in the centre plate at the top of the keel to allow the 
Jieel jpiece, or frame back bar, as it is sometimes called, to be 
fixed in position. The butts or connections of these plates com- 
prising the keel must be kept well clear of each other, and 
separated by at least two frame spaces, wherever practicable. 






Fig. 43. — Keels and Keelsons op Vabious Forms. 



The centre plate being carried up above the top of the floors 
forms part of the centre keelson. Two horizontal plates are 
then attached to the floor plates, one on each side of the centra 
plate, the connection being made by means of the reverse angles. 
To the upper edge of the centre keelson plate two angles are 



STRUCTURB. 59 

riveted, and also two others on the top of the horizontal plates. 
The combination now forms a splendid backbone to the whole 
ship. It will be noticed in ^g, 36, as also in A, B, C, D, and 
E (fig. 43), that a short piece of angle bar called a lug piece is 
attached to the top of the floors on the opposite side to the 
reverse angle, thereby ensiwing a doubly strong connection 
between the keelson and the transverse framing, for unless the 
longitudinal and transverse framings are thoroughly united, 
their separate strength is of little value to the ship as a whole, 
and they would thus fail in their chief function. 

Keelsons, — The commonest form of centre keelson consists of 
a single plate standing upon the top of the floors with double 
angles riveted to its upper and lower edges, as shown in B 
(fig. 43). In addition, a plate called a rider plate is riveted on 
the top of the two uppermost angles. The great disadvantage 
of this keelson, especially in large, heavy vessels, is, that it 
afibrds no resistance whatever to buckling of the floors, and 
thus it has often happened that when vessels of this form of 
construction have grounded upon an uneven bottom, the keel 
has been sprung up, and consequently the floors having nothing 
between them to stiffen them vertically at their deepest part, 
have buckled. This lack of stiffening between floors is the 
great defect of all keelsons standing simply upon the top of the 
floors. 

A very good kind of centre keelson is that shown in A 
(fig. 43). Here we have the deficiency in the previous keelson 
remedied. Its parts are as follows : — First, there is the deep 
bulb plate, with angles on its lower edge, attached to the top of 
the floors. Between one of the angles and the bulb plate an 
intercostal plate is let down between all the floors on to the top 
of the keel, and secured to the floors by vertical angle bars, as 
shown. 

A now unfamiliar, though very efficient, form of centre keelson 
is sometimes to be seen in old vessels. A sketch of the same is 
shown in C (fig. 43). It consists of a continuous centre plate 
extending from the top of the floors to the top of the keel, the 
latter being a broad, thick plate known as a flat-plate keel. 
On the top of the floors a thick, broad plate is laid, and attached 
to the vertical keelson plate by large, double, continuous angles, 
as shown. Since the entire centre keelson is continuous, it 
follows that the floor plates must butt on either side of it, the 
connections between the two being made by double angles. The 
vertical plates comprising the centre keelson are connected by 
double butt straps (see fig. 73), treble riveted. The horizontal 
plate is also riveted to the reverse angles on the top of the 



60 KNOW TOUR OWN SHIP. 

floors, and in addition to a short lug piece fitted on the top 
edge of the floor opposite to the reverse bar. This form of 
centre keelson is usually adopted in double bottoms (see 
^g. 55). 

In D (fig. 43) we have another modification of a centre keelson 
with a flat plate keel. The centre plate is continuous, and 
extends above the top of the floors sufficiently high to take two 
large angle bars which are riveted to two horizontal plates 
shown on each side of the centre plate, and also to the top of 
the floors. 

Keelsons and stringers are fitted for the purpose of giving 
longitudinal stiffness to the vessel, and also in order to tie or 
unite the transverse framing, so that, when strain is brought to 
bear upon any particular part, it is transmitted to the structure 
as a whole. 

Keelsons and stringers are all forms of girders (see fig. 36), 
varying both in number and size, according to the dimensions 
and structural requirements of the vessel. 

Those longitudinal stiffeners located along the bottom of the 
vessel between bilge and bilge are called keelsons ; above the bilge 
they are termed stringers. 

Stringers. — It will be noticed that wherever a tier of beams 
is fitted in a vessel, a broad, thick plate, called a stringer plate, 
is attached to its extremities, and connected w^ith the shell by 
a strong angle bar. This bar, called a sliell bar, is fitted inter- 
costally between the frames if below the weather deck, and 
to the reverse frames extending above the beams a continuous 
angle bar is riveted, and also to the stringer plate. If the 
deck is an iron or steel one, the plate at the end of the beams 
is still called a stringer plate. It is always thicker than the 
adjoining plating, and, being firmly connected with the beams 
and shell, forms a splendid longitudinal stiffener to the vessel, 
acting in conjunction with the beams and transverse framing in 
keeping out the sides of the vessel to their proper position and 
shape, and in resisting longitudinal twisting strains. 

If the beams are widely spaced and no deck is laid, the stringer 
plate is supported by means of knees or bracket plates under- 
neath. 

We observed at the beginning of this chapter that not only is 
the transverse strain greatest, but the longitudinal also, in the 
region amidships, and is gradually reduced towards the ends 
of the vessel, thus showing that a reduction may be made in the 
thickness of the material used in the construction towards the 
ends. This applies generally throughout the vessel, for, be it 
remembered, excessive strength is useless. 



STRUCTURB. 61 

Distribution of Material to Counteract Strain. — With 
such an able means of conveying instruction to our minds as the 
eye, it seems very probable that, with short explanatory notes, 
a few sketches, showing both the arrangement and growth of the 
framing and plating, ranging from the smallest to large types of 
merchant vessels, will prove of more value, and will perhaps be 
plainer than pages of printed matter. Before doing this we 
must not omit to notice that although the first aim is to secure 
the greatest possible efficiency by a judicious combination of 
longitudinal and transverse framing, yet immense strength is 
added by an efficiently worked skin, or shell plating, as it is 
more commonly termed. Some parts of this outside plating are 
capable of rendering more service to the structure than others. 

For example, the ordinary bar, or hanging keel, as it is often 
termed, has its only connection to the vessel by means of the 
strakes, or rows of plating, called the garboard strakes, on either 
side of the keel. The absurdity of connecting a thin plate to a 
thick bar with large rivets, widely spaced, will be easily under- 
stood, and thus the garboard strake is made thicker than its 
adjacent plating. Moreover, where no heel pieces are fitted, 
connecting the lower extremities or heels of the frames on one 
side of the vessel to those on the other side, the garboard strakes 
accomplish this by securing the heels of the frames firmly to 
the top of the keeL It also adds stiffness to the bottom flange 
of the ship girder. 

We have already seen the advantage of strengthening the 
upper and lower edges or flanges of a girder in increasing its 
efficiency to resist longitudinal bending; and since a ship, as 
previously stated, is simply a huge, hollow girder, any method 
of deepening it vertically (ship's side plating, etc.), or increasing 
the strength of its upper and lower flanges, must add to its 
longitudinal strength. Hence it is compulsory, if a vessel be 
classed, to have its uppermost strake of outside plating, called 
the slieer strake, and sometimes the strake next below, increased 
considerably in thickness (see ^g, 36). Also on the bottom of 
the girder, in the region of the bilge, one or two of the strakes 
are thickened in long vessels. Midway between the bilge and 
the sheer strake — approximately in the region of the neutral 
axis — where the strains vanish, the thickness of the plating is 
least. The value of long bridges extending over the midship 
length of a vessel, increasing the depth of the girder at the very 
place where the bending strain is greatest, must be evident. 
Indeed, in two- and three-decked vessels of over thirteen depths 
to length, Lloyd's require that they have a substantial erection 
extending over the midship half length. A complete or partial 



62 KNOW YOUR OWN SHIP. 

steel deck over the middle of the length, together with the 
beams, also affords great strength to the ship girder in increasing 
the efficiency of its upper flange. 

Definition of Important Terms. — It is necessary at this 
stage that a few terms be clearly understood. 

1. Length between Perpendiculars, — For vessels with straight 
stem this is taken from the fore part of the stem to the after 
part of the stern post. Should the vessel have a clipper or 
curved stem, the length is measured from the place where the 
^^^ line of the upper deck beams would intersect the fore edge of 
the stem, if it were produced in the same direction as the part 
below the cutwater (fig. 44). 




N, 



Fio. 44. — Length between Perpendiculars. 



2. " Lloyd's LengthJ' — Lloyd's length is the same as the fore- 
going, except that the length is taken from the after side of the 
stem to the fore side of the stern post. 

3. Extreme Breadth, — This is measured over the outside 
plating at the greatest breadth of the vessel. 

4. Breadth Moulded. — This is taken over the frames at the 
greatest breadth of the vessel. 

5. Depth Moulded. — This is measured in one-, two-, and three- 
deck vessels at the middle of the length from the top of the keel 
to the top of the upper deck beams at the side of the vessel. 

In spar- and awning-decked vessels, the depth moulded is 
measured from the top of the keel to the top of the main deck 
beams at the side of the vessel. 

6. Lloyd's Depth. — This is somewhat different. We have seen 
that they require a round up upon the weather decks, of a 



STBUCTXTRB, 63 

quarter of an inch to one foot of beam. This round up is added 
to the moulded depth, and gives Lloyd's depth. "XVith this 
modification it is otherwise the same as No. 5. 

In designing our series of midship sections illustrating the 
arrangement, amount, and development in structural strength 
in progressive sizes of vessels, we will consider, for the sake of 
example, that the vessels are to be classed at Lloyd's. 

The size and spacing of all transverse framing — frames, 
reverse frames, floor plates, pillars — are regulated by numbers 
obtained entirely from transverse dimensions, as follows : — 

Add together (measurements being taken in feet) half the 
moulded breadth, tlie depth (Lloyd's), and the girth of tlie half 
midship frame section of the vessel, measured from the centre 
line at tlie top of tlie heel to tlie upper deck stringer plate. By 
referring to the tables in Lloyd's rules, the sizes of these parts 
of the structure, corresponding to the sum of these dimensions, 
may be found. The number for three-deck steam vessels is pro- 
duced by the dedu^ion of 7 feet from the sum of tlie measure- 
ments taken to the top of tlie upper deck beams. 

The sizes of all longitudinal framing — keel, keelsons, stringers, 
as well as thickness of outside and deck plating, stem bar, and 
stem frame — are governed by the number obtained by multiply^ 
ing Lloyd! s first number for frames, etc, by the length of the vessel. 

Vessels of extreme dimensions require special stiffening above 
that ordinarily needed by the numbers obtained as above, and 
special provision is made for this in the rules. 



64 



KNOW TOUR OWN SHIP. 




Under 13 feet depth. 12^ depths in length. 

Fig. 45. —Dimensions of Framework and Plating fob 
Vessels less than 13 feet in depth. 



i Girth, . 
I Breadth, 
Depth, . 



Lloyd's Numerals. 



1st No., 
Length, 

2nd No., 



21-8 
120 
12-88 

46'C3 
161 

7507 



Frames, 3 x 3 x , spaced 21 ins. 

Reverse frames, 2J x 2J x ^f^. 
Floors, 13 X ^ ~ ^ 



20 
Centre keelson, 11 x 



9-7 
"20~' 



Keelson continuous angles, ZixZx-^Q, 



Beams, 5J x ^ - bulb plate with 
Double angles, 2^ x 2^ x ^. 

Sheer strake, 32 x -^-^ ~ ^ 



Garboard strake, 31 x 



20 ■ 
9-8 

"20"' 



Stringer plate, 36 x -^^y - 19 x ■^. 
Gunwale angle bar, 8 x 8 x |^. 
Keel, 7 x If. 



Additions for Extreme Length, 

To thickness of sheer strake, ^ is added for | L amidships. 

To bilge keelson, a bulb plate is added for f L amidships. 

To thickness of 2 strakes at bilge, -^ is added for } L amidships. 

Abbreviations. 

L means length, thus 
} L amidships ,, three-fourths length amidships. 
R „ reserve frame height. 
8-7 



20 



II 



thickness reduced from ^ to ^. 



Note, — All sizes of plates and angle bars are given in inches. 



STBUCTUBE. 



05 




Under 14 feet depth. 12^ depths in length. 
Fio. 46. — Dimensions op Framework and Plating for 



Vessels less than 14 feet in depth. 
Lloyd's Numerals. 



i Girth, . 
I Breadth, 
Depth, . 



1st No., 
Length, 



24 

13-5 

13-83 

51-33 
173 



2nd No., 8880 

6 - 5 ■ 



Frames, 3 x 3 x 



20 



., spaced 21 inches. 



Reverse frames, 2^ x 2} x ^. 
Floors, 14i X ^ " ^ 



20 
Centre keelson, 12 x 



9-7 
20 • 



Keelson continuous angles, 3^ x 3 x -^V 

Hold pillars, 2^. 
Sheer strake, 33 x "^^ 



Garboard strake, 32 x 



20 
9-8 



20 



Deck stringer plate, 38 x ^^ - 20 x ,%. 
Gunwale angle bar, 3 x 8 x ^. 
Keel, 7J x IJ. 

Additions for Extreme Length, 

To thickness of sheer strake, -^ is added for | L amidships. 

To bilge keelson, a bulb plate is added for f L amidships. 

To thickness of 2 strakes at bilge, ^ is added for i L amidships. 

B 



66 



KNOW TOUR OWN SHIP. 



^ MX i I II I ■ ■■II I II I I p oxg 




lea 




Under 16^ feet depth. 12} depths in length. 

Fig. 47.— Dimensions op Framework and Plating Foa 
Vessels less than 15} feet in i>epth. 

Iiloyd's Numerals. 

i Girth 26'5 

I Breadth, 14*5 

Depth, 16-33 



1st No., 
Length, 

2nd No. 



66-33 
192 



. 10816 



6-5 
Frames, 3J x 3 x — — — , spaced 22 inches. 

Reverse frames, 2 x 2^ x ^q. 
Floors, 16 X ^ " ^ 



20 • 
Centre keelson, 12 x 



10-8 
20 • 



Keelson continuous angles, 4^ x 3 x /q. 
Hold pillars, 2f . 

Beams 7 x ^, " bulb plate with | ^^^^^ 
Double angles, Z x B x J^^ J *"»'^*"»«'« "»*"«* 

Sheer strake, 34 x ^^ " ^ 



Garboard strake, 32 x 



20 
9-8 

~20"' 



Deck stringer plate, 40 x -^jj - 22 x /^y. 
Gunwale angle bar, 3^ x 3| x Z^. 
Keel, 7i x 2. 

Additions for Extreme Length, 
To thickness of sheer strake, -^ is added for | L amidships. 
To strake below sheer strake, 4is is added for ^ L amidships. 
To bilge keelson, a bulb plate is added for f L amidships. 
To thickness of 2 strakes at bilge, ^ is added for i L amidships. 




67 



Under 16} feet depth. 12} depths in length. 

FiQ. 48. — DiMBNSiONS OF Frambwoek and Plating fob 
Ybssbls lbss than 16i fbbt in dbfth. 

Iiloyd's Numerals. 

i Girth, 28-3 

i Breadth, 15*5 

Depth, . . . . . . . 16-33 



1st No., 
Length, 



60-13 
205 



2nd No 12326 



7 — 6 
Frames, 3} x 3 x 1 r, spaced 22 inches. 

Beverse frames, 3 x 2^ x |/\). 
Floors, 17i X ^ " ^ 



20 

Centre keelson, 13 x 



10-8 



Keelson continuous angles, 4} x 3} x -f^. 

Main deck beams, 7i x A, bulb plate with \ -Uemate frames 

Double angles, 3 x 3 x A J ^^^^^^^^ "*'"®^- 

Hold beams, 8 J x -^^ bulb plate with \ on every 10th 

Double angles, 4 x 3 x /o, with covering plate J frame. 
Main deck stringer plate, 44 x ^ - 24 x j^. 
Hold stringer plate, 27 x -^ - 21 x A. 
Gunwale angle bar, 4 x 4 x -A. 

Sheer strake, 36 x ^^ ~ ^ 



Garboard strake, 33 x 



20 
10-9 

"■20"' 



Keel, 7J x 2J. 
Hold pillars, 2|. 

Additions for Extreme Length, 

To thickness of sheer strake, ^ is added for | L amidships. 
To strake below sheer strake, -^ is added for ^ L amidships. 
To bilge keelson, a bulb plate is added for ^ L amidships. 
To thickness of 2 strakes at bilge, ^ is added for ( L amidships. 



68 



KNOW YOITB OWN SHIP. 




Under 23 feet depth. 12^ depths in length. 
Fig. 49.— Dimensions of Framework and Plating foe Vessels 

LESS than 23 FEET IN DEPTH. 



STBUCTURB. 69 



liloyd^s Numerals. 

J Girth .88 

I Breadth, 19 

Depth, 22*83 

1st No., 79-83 

Length 286 

2nd No., 22831 

8 — 7 
Frames, 5 x 3 x , spaced 24 inches. 

Reverse frames, 3^ x 3 x ^7. 

Floors, 24 x l^-ZA. 
' 20 

to _ It 

Centre keelson, 20 x i^ —, 

20 

Keelson continuous angles, 6 x 4 x /^« 

Intercostal keelson plate, •^« 

Complete steel deck, ^ thick on main deck. 

9 — 8 
Main deck heams, 6^ x 3 x , bulb angle on every frame. 

Hold beams, 10 J x ^ bulb plate, with \ ^verv 10th frama. 
Double angles, 4i x 4 x ^% r^ ®^®^^ ^^'^ "^^^ 

Main deck stringer plate, 41 x ^ - 35 x ^, 
Hold stringer plate, 38 x -^ - 29 x ^fy. 
Gunwale angle bar, 4^ x 4^ x ^. 

Sheer strake, 42 x ^^ ~ "^^^ 
' 20 

12 — 11 
Garboard strake, 36 x — — — ^ 

Eeel, 10 X 2}. 
Hold pillars, 3^. 

Additions for Extreme Length, 

To thickness of sheer strake, ^^ is added for | L amidships. 
To strake below sheer strake, ^^ is added for ^ L amidships. 
To bilge keelson, a bulb plate is added for f L amidships. 
To thickness of 3 strakes at bilge, -j^ is added for J L amidships. 



70 



KNOW TOUR OWN SHIP. 




Under 26 feet depth. 

16 depths to middle deck in length. 

11*6 „ upper 



II 



FiQ. 50.— DiBfBNSiONS OP Pramework and Plating for Vessels 

LESS THAN 26 FEET IN DEPTH. 



STRUCTURE. 71 



Lloyd's Numerals. 

i Girth, 4075 

* Breadth, 20*5 

Depth, 25-83 



87-08 
7 



1st No., 8008 

Length, 301 



2nd No., 24104 



8 — 7 
Frames, 5 x 3J x ■ spaced 24 inches. 

Reverse frames, 3} x 3^ x ^^. 
Floors, 24J x ^^^^T^. 

Centre keelson, 25 x — - — • 

20 

Keelson continuous angles, 6^ x 4 x ^V 

Intercostal keelson plate, ^. 

Complete steel deck, ^ thick on main deck. 

10 — 9 
Upper deck heams, 7J x 3 x — — - — bulb angles on every frame. 

^\) 

Middle deck beams, 10 x ^J, bulb plate with Ion every alternate 
Double angles, 3^ x 3i x ^ / frame. 

Hold beams, 11 x ^, bulb plate with J . ., - 

Double angles, 5x4x3^ { °" ®^®^y ^®^^^ "*"^®- 

Upper deck stringer plate, 43 x ^^ - 36 x ^^. 

Miadle deck stringer plate, 62 x ^ - 36 x -^q. 

Hold stringer plate, 40 x ^^ - 31 x ^. 

Gunwale angle bar, 4^ x 4^ x 1%, 

Sheer strake, 42 x — - — . 
' 20 

12 — 11 
Garboard strake, 36 x i__ ^_. 

* 20 

Keel, 10 X 2f. 

Hold pillars, 3|. 

Additions for Extreme Length. 

To thickness of sheer strake, ^ is added for | L amidships. 
To bilge keelson, a bulb plate is added for f L amidships, and 

an intercostal plate for J L amidships. 
To thickness of 2 strakes at bilge, -^ is added all fore and aft. 
Centre keelson increased in depth. 
To side keelson, a bulb is added for i L amidships. 
To bilge stringer, an intercostal plate is added for | L amidships. 



72 



KNOW TOUR OWN SHIP. 




Under 86 feet depth (also nnder S9 feet). 
15*5 depths to middle deck In length. 
12 '5 ,f upper „ 

Fia. 51. — Dimensions of Framework for Vessels less than 

36 FEET IN depth. 

Note.— The scantlings are for the vessel nnder 36 feet depth, all of which are shown in 
clear, black lines. The tig. is drawn to the under S9 feet depth in order to show the 
introduction of the new tier of beams indicated by dotted lines. Such a Teasel would 
rec^uire both additional topside and bottom strengthening. 



STRUCTURB. 73 



Lloyd's Numerals. 

_ Girth, 62-6 

* Breadth, 25 

Depth, 85*83 

113-33 
7 

IstKo., . 106-33 

Length, 448 

2nd No., 47635 

Frames, 6 x 34 x ~ , spaced 25 inches. 

Reverse frames, 4} x 3^ x ^^. 

Floors, 32 x l ^' ^ . 
* 20 

Centre keelson, 36 x ~ . 
* 20 

Keelson continuous angles, 6^ x 4| x ^. 

Intercostal keelson plates, ^. 

Foundation plate, 18 x \%, 

Complete steel deck to upper deck, -j^^. 

Complete steel deck to middle deck, •^. 

12 — 11 
Upper deck beams, 9 x 3 x — Kfr—> ^^^ angle on every frame. 

12 — 11 
Middle deck beams, 9 x 3 x — , bulb angle on every frame. 

Lower deck beams, 12 x ^, with \ ^^ ^„«.^ o^a Aw.*»<> 
Double angles, k x 3 J x ^ T^ ^^^^ ^^^ ^^"'^ 
Upper deck stringer plate, 64 x ^ - 51 x ^. 
Miadle deck stringer plate, 64 x ^ - 51 x ^V 
Lower deck stringer plate, 56 x ^ - 44 x A. 
Gunwale angle bar, 5 x 5 x ^^. 

Sheer strake, 46 x i^^— . 
' 20 

Garboard strake, 36 x _~ _. 

20 

Keel, 12 x 3J. 

Hold pillars, 4. 

Additions for Extreme Length. 

Sheer strake doubled for whole width, for f L amidships. 
To strake below sheer strake, -^ is added for L amidships. 
To upper deck stringer plate, -^ is added for f L amidships. 
To side keelson, continuous plate is added for f L amidships. 
To bilge keelson, continuous plate is added for ^ L amidships. 
To bilge stringer, intercostal plate is added for | L amidships. 
Centre keelson increased in depth. 



74 KNOW YOUB OWN SHIP. 

Relation of Strength to Dimensions — Notes on "Mid- 
ship Sections.** — In considering the subject of strains, it was 
found that both longitudinal and transverse strains decreased 
towards the ends of the vessel, being greatest on each side of mid- 
ships. Naturally, therefore, in turning to the transverse sections 
(figs. 45 to 51), we expect to find a corresponding arrangement 
of structural strength. Such, indeed, is the case. In the trans- 
verse framing the frames and floors maintain their maximum 
size for three-fifths of the vessel's length amidships, and are 
reduced in thickness for the remaining one-fifth of the length 
at each end. The floors are carried up the bilge to a height of 
twice their midship depth above the top of the keel, for one- 
fourth of the midship length of the vessel. Fore and aft of this 
distance, the ends are gradually lowered until the tops of the 
floors are level. At the extreme ends, however, the floors are 
increased in depth, as subsequently shown. 

The height to which the reverse frames are carried varies 
according to the transverse dimensions of the vessel. When 
Lloyd's first number is below 45, the reverse frames are carried 
across every floor plate, and up the frame to the upper part of 
the bilges ; when 45 and below 57 they extend alternately to 
the gunwale, and high enough to enable the double angle 
stringer above the bilges to be securely connected; or, if hold 
beams are fitted, high enough to get a good connection to the 
beam stringer angle. When the number is 57 and above, the 
reverse frames extend alternately to the gunwale and the 
stringer next below. When the number for sailing vessels 
reaches or exceeds 75, the reverse frames extend to the gun- 
wale on every frame. 

Except in spar- and awning-decked vessels, and in poops and 
forecastles, the beams, exclusive of hold beams, where less than 
three-fourths the length of the midship beam, are somewhat 
reduced — in many cases — in both depth and thickness. 

In the vessels of which figs. 45, 46, and 47 are midship 
sections, only one tier of beams is required; but immediately 
the depth reaches and exceeds 15 feet 6 inches (Lloyd's depth), 
a tier of widely-spaced hold beams is fitted (figs. 48 and 49), 
with a continuous stringer plate on the ends. This, together 
with the gradual growth of the other framing, provides the 
additional transverse and longitudinal strength demanded by 
greater depth and length. When 24 feet is reached and 
exceeded, another tier of beams is required (fig. 50). 

When the depth reaches 32 feet 6 inches, although another 
tier of beams is not required, a stringer plate supported on 
alternate frames by large bracket knees has to be fitted, and on 



STRUCTITRB. .75 

its inner edge is riveted a large angle of the size of the centre 
keelson angles, converting it still further into an efficient girder. 

"When 36 feet depth is reached, the additions shown by the 
dotted lines in fig. 51 are required. Here we have a fourth 
tier of beams of extra strength fitted to every tenth frame. 
These are known as orlop beams. 

Turning to the longitudinal framework, we find similar reduc- 
tions in the scantlings taking place. The centre keelson plate 
standing upon the top of the floors, together with its rider plate, 
maintains the midship thickness for (me-half the vessel's length 
amidships. Beyond this length considerable reduction takes 
place in the thickness, and the rider plate disappears altogether 
before and abaft of the three-fourths length amidships. Stringer 
plates at the ends of beams retain their midship dimension for 
one-half the vessel's length. Throughout the remaining one- 
fourth length at each end they gradually diminish in both 
breadth and thickness. The number of hold stringers and 
keelsons to below the bilge is regulated entirely by the depth 
of the vessel. The sizes of all the large angles for keelsons and 
stringers in the hold are the same as the centre keelson angles. 

A glance at the outside shell plating covering the frames also 
shows a reduction, and this takes place on the one-fourth length 
at each end. 

Where a steel deck of seven-twentieths of an inch or over is 
fitted, it is reduced in thickness fore and aft of the half length 
amidships. A little consideration will soon make it obvious 
that it would be absurd to deal out to every vessel of similar 
" 2nd numerals " exactly similar longitudinal strengthening, for 
then a long, shallow vessel would receive actually less longi- 
tudinal stiffening than a shorter, deep one, since the introduc- 
tion of hold stringers and keelsons is regulated almost entirely 
by the depth. 

We have already seen that long, shallow vessels with small 
depth of girder possess less resistance to bending than shorter 
ones, not to mention shorter and deeper vessels. It is, there- 
fore, the custom with classifying associations to ^^ upon a 
standard vessel of a certain number of depths to the length. 
Lloyd's Committee adopt a length of eleven depths as the 
standard worked upon. Vessels exceeding these proportions 
are, therefore, subject to the introduction of additional longi- 
tudinal strengthening over the middle of the length. In figs. 
45 to 51, the number of depths in length is 12*5, excepting fig. 
50, which is 11-6, and the additional strengthening therefore 
required is shown, as far as possible, on their respective 
sketches, as well as in the table of additions on each diagram. 



76 KNOW YOUB OWN SHIP. 

When in three-decked vessels the length is more than eleven 
times the depth taken from the top of the keel to the top of the 
middle deck beams, special additional strength has to be introduced 
at the bilge and bottom. Such strength has been introduced 
into the foregoing midship sections. All vessels having a length 
of thirteen or more times the depth from the top of the keel to 
the top of the upper deck beams are to have a substantial erec- 
tion, such as a bridge, extending over the half length of the 
vessel amidships. 

A perusal of figs. 45 to 51, with the scantlings accompanying 
them, will, it is believed, fully verify the foregoing remarks upon 
the arrangement and growth of structural strength. 

Local Strengthening — Space occupied by Machinery. — 
Engine and Boiler Space, — Perhaps one of the first things which 
strikes one in studying the arrangement of a steam vessel, from 
a structural point of view, is the concentration of weight, and 
also the vibration, especially in vessels of high speed, in the 
machinery space. In addition to this, there is a break in the 
arrangement of transverse strength owing to the omission of 
beams, and even at the upper deck the beams are cut in the way 
of the engine and boiler casings. The result of all this is to 
produce a tendency to vertical elongation, and to cause the 
upper breadth of the vessel to contract. 

Moreover, if the vessel did not possess sufficient rigidity and 
stiffness to resist working under the vibration of the engines, 
the evil would rapidly increase, and assume serious dimensions. 
But, happily, all this can be provided against, and although the 
methods adopted may vary somewhat for different types of 
vessels, yet a few general hints may be given. 

First of all, a good foundation must be secured for both' 
engines and boilers. Lloyd's require that floor plates under 
engines be one-twentieth of an inch thicker, and under boilers 
two-twentieths of an inch thicker than are otherwise required, 
and by this means greater stiffness is given to the bottom of the 
vessel. No doubt the extra one-twentieth put upon boiler 
floors is on account of the fact that the damp heat created there 
has the effect of making corrosion more rapid than elsewhere. 
At the same time, it should be noted that a great deal of the 
corrosion in this locality is due to neglect, for if the bottoms of 
vessels were carefully watched, and frequently cement washed, 
there would be less cause for complaint regarding the condition 
of the floors of comparatively new vessels, and it would be found 
that a little care is cheaper in the end than new floors. As a 
rule, it is found, in vessels with ordinary floors, that the engine 
foundation or seat, as it is more commonly called, has to be built, 



Engine seat. 



77 




Blevatioib 
SHCt-k. 




flan. 




Section. 

Fig. 52.— Engine Seat. 



I 



78 



KNOW YOUB OWN SHIP. 



to a height considerably above the floors. When this is the case, 
and it is practicable, a splendid seat is constructed by making the 
floors deep enough to reach to the engine seat, and to extend with 
horizontal edges from side to side of the vessel. Across the top of 
all floors in engine and boiler space, Lloyd's require double reverse 
angles to be fitted at least from bilge to bilge. This not only 
stiffens the floor, but forms a good means of connection for the 
thick plating to which the bed plate of the engine is bolted. 
Intercostal plates, fitted between floors, on either side of the 




FiQ. 53. — ^Tbotjgh ttndeb Engines to catch Grease Drip. 



centre line, give further stifihess to the floors, and support for the 
condenser, etc. (see fig. 52). 

Sometimes, especially in the case of yachts, a watertight trough 
is fitted in the engine floors immediately under the shafting, 
which prevents the grease drip from the engine finding its way 
into the bilges (fig. 53). 

Where the floors are not made continuous from keel to engine 
seat, and from bilge to bilge, a seat has to be built simply in the 
way of the engine on the top of the ordinary floors; this, however, 
lacks in efficiency as compared with the previous method. 

The boilers, too, require to be fitted on foundations which are 
firm and rigid, and securely connected with the bottom of the 
vessel (fig. 54). This is done by fixing two or three thick plates 
called stools^ to the top of the floor plates under each boiler. The 



STRUCTURE. 



79 



top edges of these plates are cut to shape so as to receive the 
boiler. They are attached to the double reverse angles on the 
top of the floors by means of double angles, and roimd thehr edges 
are fitted large double angles. These provide a good surface 
upon which the boiler can rest. Then, to hold the stools in place 
and prevent them tripping— that is, inclining one way or 
another— tie ])lates are fitted fore and aft, and connected to the 
double angles. In the case of vessels constructed with double 
bottoms, for water ballast, as shown in fig. 55, the engines 
generally stand upon the tank top, this usually being of sufficient 
height. Sometimes, however, it is necessary to build a girder seat 
upon the inner bottom plating, in order to raise the engines to the 
desired height In any case, the inner bottom plating is increased 




Fio. 64.— Boiler Stool. 



in thickness in way of the engine and boiler space, and immediately 
under the engines a thick foundation plate is firmly riveted. 
This plate may form a part of the inner bottom plating, or may be 
riveted on the top of the inner bottom plating when the engines 
stand immediately upon the tank top, or it may be riveted to the 
top of the girder seating when such an arrangement exists. To 
this the bed plate of the engine is bolted. The boiler stools are 
riveted to the inner bottom plating. As in the case of ordinary 
floors, extra stiflening is required at the bottom of the vessel 
under the engines and boilers, and this is done by fitting inter- 
costal girders. 

Having stiffened the bottom of the ship, it is necessary to 
provide for the loss of the beams, and also some means of keeping 
out the sides of the vessel This is done in exactly the same 



80 



KNOW YOUB OWN SHIP. 



manner as when hold beams are dispensed with — viz., web frames 
are fitted. In high speed vessels especially, care should be tak^n 
that sufficient of these are introduced. Valuable as web stringers 
are, in conjunction with web frames, it is found better in the 




Fig. 55. — Midship Section of a Vbssbl built on the "Deep Fsams" 
Ststem with a Cellulab Double Bottom. 

machinery space to fit extra strong beams wherever practicable. 
Several forms may be adopted, according to the size of the vessel 
(see B, C, D, E and F, fig. 32). 

It will often be found of advantage to further stiffen the frames 
in the engine and boiler space by fitting all the reverse angles to 



STRUCTURE. 



81 



the upper deck, and in some cases the double reverse bars 
also. 

Sometimes in vessels with the centre keelson fitted on the top 
of the ordinary floors (fig. 56), the height of the keelson throws 



FUKTtL - 





Intercostal plates shown by crossed, dotted lines. 

Fig. 66. — Intercostal Compensation fob Reduction in Depth 
OF Centre Keelson under Boilers. 

the boiler or boilers too high, and it is necessary to cut the keelson 
down. Were no compensation made for this reduction in the 
height of the girder, the weakness at this part would be a most 
serious defect. Several means, however, may be adopted to recover 
the strength. 

In the first place, it will be seen that, owing to the depth of 
the keelson being reduced, the sectional area of the keelson is 
reduced also. This may be recovered by making the central plate 
thicker at this part until the sectional area has been regained. 
But even this does not fully recover the loss of strength, for 
though the sectional area is obtained, yet the reduced depth of 
the girder proves a loss of strength in resisting longitudinal bending. 
It, therefore, becomes necessary to increase the sectional area to 
beyond what it was in its original condition. A good method of 
compensation is to fit intercostal plates between the floois, and 
attached to the centre plate by means of its lower angles, as shown 
in fig. 56. 

Again, it sometimes happens that, in the way of the boilers, 
it is necessary to reduce the width of the hold stringer plates. 
Compensation may be made, as in keelsons, by increasing the 
thickness of the plate in the way of the reduced width, and also 
by fitting strong angles on the inner edge of the stringer plate. 

Mode of Strengthening Ship at Aft End of Shafting. — 
Leaving the engine and boiler space, and travelling aft, great 
vibration and strain is thrown upon the vessel, especially when 
in a seaway, by the action of the propeller. At one moment it is 

F 



82 KNOW YOUR OWN SHIP. 

totally submerged, and revolves with regular precision, but imme- 
diately after the wave has passed, it is totally or partly out of the 
water, and races at a high speed. Provision must, therefore, be 
made for this. To stiffen the sides of the vessel, the floor plates 
at the aft end should be made considerably deeper, and towards 
the stern post they should be carried above the shaft, so that the 
shaft passes through them. Then, again, it is most important 
that a sound connection be made between the outside plating and 
the stern post. By the midship sections we see that considerable 
reduction takes place in the thickness of the end outside plating. 
To connect thin plating to a massive iron stern post with large 
rivets widely spaced would, it is likely, result in the thin plate 
being unable to hold the stem post rigid under the strains men- 
tioned, and leakage would ensue. So what is done is to increase 
the thickness of these endmost plates to at least the thickness of 
the plating at midships, and thereby get a more evenly balanced 
connection. 

But a further means of rigidly fixing the stem frame is re- 
quired, and this is done by fitting a deep plate, called a transome 
plate, against the upper part of the stern post, extending across 
the counter from side to side, and riveted to the frames. The 
connection between the stem post and the transome plate is 
effected by means of strong angles (see fig. 57, section A B). 

It is well known to seamen that considerable leakage often 
takes place, notwithstanding these precautions to hold the post 
fixed. An additional means to secure this end is to have another 
post carried up at the fore side of the stern frame (Y in sketch), 
and this also is attached to a stout plate carried from side to 
side of the vessel, and connected with the frames as well as to 
a bracket plate at the lower deck. By this method, with sound 
workmanship, and by filling in the space above the propeller 
aperture between the two parts with cement, leakage is very 
improbable. 

In the case of steamers with twin screws, a different arrange- 
ment of supporting the end shafting has to be adopted. One 
method, after leaving the skin of the ship, is by projecting struts, 
as shown in fig. 58. 

The importance of having these struts securely attached to the 
hull of the vessel will readily be observed, for should any accident 
happen here, the vessel is entirely crippled. When the screws 
somewhat overlap each other, and revolve partly in an aperture 
in the stern frame, a sound and reliable connection of the struts 
with the stern frame may be made, as shown by fig. 58, a and 6, 
the ends of the struts being welded out into broad palms capable 
of taking a sufi&cient number of rivets. If there is a weak point 



STRUCTURE. 



83 



in this method, it is in the fact that both the upper palms of the 
struts, and also the lower palms, are connected by the same rivets, 
so that on each side of the main post, owing to the vibration of 
the shafts, there is this tendency to work or shear the rivets. 
Each rivet, therefore, bears a double strain. But where no aper- 
ture is needed for the propellers, the shell plating is carried out 
to the after stern post, and another means has to be provided for 
the connection of the struts. The commonest way, perhaps, is 
that shown in fig. 59. 

Here the upper palms are simply fixed on to the outside shell 




/DECKi 



"^braCkkt PLATR 

CONNECTING POST 
TO OCCKBCAM 



SECTION A.e. £NLARCED 

RUDDER POSr 
8TERN POST 



RUDDER 
TRUNK 




TRANSOMS PLATCi 



TffANSOME 
PLATE 



LOWER D? 




BRACKET PLATE' 



8CARPH 



ENLARGED 
(/ VIEW AtY 
LOOKING APT 



Fio. 57.— Ste&n F&ame and Connecxiun. 



plating. If this were all the connection, it would not take a keen 
observer to see that the immense vibration of the shafting, especi- 
ally in high-speed steamers, would simply tear away the plating. 
It therefore becomes absolutely essential that the most effectual 
means be adopted to secure the best and surest connection. Two 
things have to be aimed at in accomplishing this. First, that at 
the point where the shafts emerge from the hull, the vessel be 
well stiffened and bound together, so as to reduce the vibration to 
a minimum ; and second, that in the way of the strut connections 
the ship be well strengthened. A variety of means may be used 



84 



KNOW YOUR OWN SHIP. 




^eCTlOHTKROUCII 
.A. B. 

n 







SHCLL 
PLATINQl 



/ 



PAL^nS FOR 
STBVTS 



STRUT 



(a) Elevation. 




(b) Transverse Section. 



Fig. 58.— CoNiTECTiON of Struts with Stern Frame in Twin-screw 
Steamers — a, Elevation; b, Transverse Section. 



BTBUCTUBB. 8S 

to attain the former of these. For example, in some veBsels the 
method shotca in fig. 69 might be eanied out. 

Here a very thick plate or neb is placed across the ehip from 
side to side, and securely riveted to the main frames (A in fig. 
60). Through this plate the shafts pass. If the vessel be not 
too vide at this part, this alone will form an efficient tie to the 
two sides, and give the required stifiness. However, in larger 
vessels, where the screws are further apart, it would be necessary 



r ' pl«t-*--»»> 




:^ 



tUEVATtON 




to further stiffen this web by means of angle bars or bulb angles 
across its face, or even introduce more of these web plates on 
adjacent frames. 

in way of the struts, the following system might be em- 
ployed : — 

1. Carry up all the floor plates from the stem post, to a few 
frames forward of the struts, above the height of the upper palms 
(«ee fig: 69). 



86 



KNOW YOUR OWN SHIP, 




»Ck 




"A 

» 

< 
H 
H 

Q 
H 

O OQ 



O 
H 



O 

Q 
O 






to 

•-4 



BTRUCTURB. 87 

2. If possible, arrange for a double frame on each side of the 
vessel to come in the centre of the palms, having thick, broad 
flanges against the outside plating. 

3. If the strake of plating, upon which the palms of the struts 
rest, be an outside one, fit a doubling plate between the edges of 
the two adjacent strakes, extending fore and aft from the after side 
of the frame abaft to the fore side of the frame before the double 
frame angles. 

If the strake of plating be an inside one, the doubling plate 
may be fitted on the outside of the shell plating. With this 
additional strengthening, the palms can now be securely attached 
to the plating with rivets, through the shell plating, doubling 
plate, and large double-frame angles. Athwartship, the vessel 
is strengthened by the deep floor plates already mentioned. 

In any case, in steam vessels there would be a watertight 
bulkhead at some little distance forward of the struts. But 
where in such vessels as these there is the greater possibility of 
leakage, it would be well to construct a watertight flat at a small 
height above the upper palms of the struts, so that, if leakage did 
occur, only this compartment would be flooded. From this 
bulkhead, it would also be well to continue the watertight flat 
just above the shafting, and extend it far enough forward to 
include the point where the shafts emerge from the shell, since 
this is another place where leakage might take place (A in fig. 59). 
This method of strut connection has the advantage of having 
the strain of the vibration of only one of the shafts thrown upon 
the rivets connecting the palms with the hull, each upper palm 
being a separate connection. 

Another method of strut connection is that shown in fig. 60, a 
and h. 

In this case, the struts are carried through the outside plating, 
and attached to a very thick intercostal plate, fitted between thick 
transverse plates. To insure watertightness where the struts 
pierce the shell, collars would have to be wrought and carefully 
caulked ; and the chambers into which the struts enter should be 
made watertight also. This method has the same disadvantage 
mentioned in fig. 58 — viz., the same rivets connect both palms. 

A system has been adopted in recent years of supporting the 
end shafting in large twin-screw vessels, on first leaving the main 
body of the hull, by carrying out the framing and shell plating 
round the shafting. Further aft, however, where the shaft is con- 
siderably out from the hull, the main frame is carried down in 
the usual way (fig. 61), and a piece of frame bar is scarphed on 
to the main frame, which, together with the shell-plating, is 
worked round the shaft, binding the projection to, and, indeed, 



88 



KNOW YOUR OWN SHIP. 



making it an integral part of the structure. By this method the. 
struts are dispensed with, and a strong and efficient means of 
supporting the shafting is obtained. 






^ 


// 




/ 


o 




y-k 




H 




-< 




> m 


^ 


^ H 


h) D 


mt 


(z) ^ 


o 


H 


<o 


h3GQ 




•< ^ 


rt 


^- s 


h-« 


O ® 


N 


•-I 




H 




o 




bq 




03 



^^^ WATERTICMT CKAMB£Rfll 




Enlarged plan of fig. 60, & 



Fig. 60, 6. —Struts cabbiet) through Shell Plating into 
Watertight Chamber (Plan). 

Panting. — Several means may be adopted to prevent panting, 
a few of which we shall notice. The common method is to fit 
plate stringers, called 'panting stringers^ in addition to the ordinary 



STRUCTURBL 



89 



stringers of the vessel, extending from abaft the collision bulk- 
head continuously into the stem, where they are joined by means 
of a plate called a breast hook, uniting, as it were, the two breasts 
of the vessel. These stringer plates are supported on beams, as 
shown in fig. 62. 

An objection raised against this method of stiffening is that it 
forms an isolated rigid girder 
and the vessel is inclined to fall 
hollow on each side of it, especi- 
ally if subject to encountering 
ice, as in the Baltic at certain 
seasons. What is wanted is 
a more even distribution of 
strength. This may be obtained 
by a slight modification in the 
arrangement of the transverse 
framing. The usual practice is 
to space the frames of a vessel 
throughout the length at equal 
distances apart, and measured in 
a fore and aft direction on the 
top of the keel. Let the frame 
spacing, as required by Lloyd's, 
be 24 inches. While the dis- 
tance from heel to heel of the 
respective frames may measure 
exactly 24 inches as they stand 
upon the keel, yet, especially in 
very bluff-ended vessels, at water- 
planes above the keel, where the 
shell rapidly curves in to the 
stem and stem, it may be found 
that the frame spacing measures 
as much as 26 inches — actually 

further apart than at amidships. Figures 62 and 63, which 
represent a somewhat fine-ended vessel, will, however, illustrate 
this. To give stiffness to the fore end, the frames should be spaced 
rather more closely instead of more widely, so as to produce, say 
2 or 3 inches less than Lloyd's requirements when measured on 
the shell. It will also be found of advantage to increase the thick- 
ness of the shell plating. Whatever method be adopted, it is advis- 
able to considerably increase the depth of the fore end floors. 

The introduction of a few extra beams with stringer plates on 
their ends, where the ordinary stringers are widely spaced, will 
generally give sufficient stiffness. 




Fig. 61.— Method of nisrENsiNa 
WITH Struts in Twin- Screw 
Steamers. 



KKOW sons OWN SHIP. 





Fio. 63— Plas op Pabtikq Smixci 



STRUCTURE. 91 

Deck Cargoes and Permanent Deck Weights. — To pro- 
vide against the strain caused by the weight of heavy timber or 
other deck cargoes, the important point to be observed is that 
the beams are held rigidly in place at their centres ; it is only 
when the deck sinks at the centre that any damage can be 
wrought upon the beam knees. Therefore, to provide efficiently 
against these strains, extra strong stanchions should be fitted under 
the beams, with well-formed heads, and spaced not more than two 
frame spaces apart. Where heavy permanent weights are carried 
on the deck, such as winches, windlass, etc., local strength may be 
obtained by fitting extra strong beams supported by additional 
pillars. 

Strains from Masts due to Propulsion by Wind. — The 
important point to be aimed at in this case is to transmit, especi- 
ally in the case of vessels propelled wholly by wind, the immense 
strain which is thrown on to the hull, so as to make it as general 
as possible, though it is classed as a local one. This is accom- 
plished by making good three conditions — 

1. That the heel or lowest extremity of the mast be firmly 
secured and rendered immovable. If the mast is stepped on the 
top of a centre keelson, the heel may be secured as shown in ^g. 
64, a thick plate being firmly attached to the top of the centre 
keelson, with a circular, welded bulb angle well riveted on its 
upper face, into which the heel of the mast is stepped and firmly 
wedged. The mast is prevented from working at its lower 
extremity by means of a piece of T-bar riveted to the centre 
keelson, and notched into the mast heel. 

2. That the mast be thoroughly secured at the upper deck. 
Since a great part of the strain is encountered here, it follows 
that the means to counteract it should be most efficient. If the 
deck is plated with iron or steel, and the plate in way of the mast 
is of reasonable thickness, a stout, circular, welded angle bulb to 
receive the wedging round the mast at the deck will provide a 
satisfactory means of transmitting the strain to the deck as a 
whole. Should, however, the deck not be entirely plated, a stout 
I)late, called a mast partner, should be attached to the beams 
round the mast, which in its turn should be efficiently attached 
to the neighbouring beams and stringer plates by tie plates, as 
shown in fig. 65. In this way, again, the strain is transmitted 
to the deck as a whole. 

3. That the upper reaches of the mast be held firm, and pre- 
vented from workinpr. This is done by having a sufficient number 
of widely spaced shrouds. 

Types of Vessels. — It is scarcely necessary to remind any 
reader that all vessels are not built for the same purposes, nor 



92 KNOW TODB OWK SHIP 

to eogstge in the same trades, or for tbe same claaa of harbours. 
Naturally, therefore, one vessel cannot fulfil all requirements, and 
be adapted for all traffio, and the result is a considerable variety 
in the types of Teasels built. It is not uncommon to hear the 
complaint lodged against a vessel that she is ill adapted for her 




special trade, and the reason undoubtedly is, in many cases, 
attributable to the fact that the wrong type has been selected to 
comply with the necessary requirements, neither the shipbuilder 
nor the naval architect with their wider experience, having been 
consulted on the matter. Type, in the majority of cases. 



BTR0CTUER. S3 

depends entirely upon deadweight and internal capacity. The 
heaviest cargoes, in comparison with their bulk, require the 
least hold space. With the majority of cargoes it is quite 
■ ■ i to design and fix upon a type of Teasel, so that, when 




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It 


r 




r 


\ 


i ! 


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Q. 






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the holds are ^lled, she will float at het load water mark. But 
it must also be obvious that there are some cargoes, such as 
metal and ores, with which it would be impossible to fill the 
hold apace, and not submerge the disc or eitreme load line at 
the load water mark. However, for all purposes, theie ia a type 



94 KNOW YOUR OWN SHIP. 

of vessel most adapted for a particular kind of cargo. "With 
light cargoes of small density which fill the holds and still leave 
large freeboard, the shipowner does not mind so long as the 
freights are satisfactory ; but naturally, when he gets cargoes of 
greater density, which bring the vessel down to the waterline 
obtained by the lighter cargo before her holds are filled, he 
desires to decrease the freeboard, and to continue to decrease it 
as the cargoes increase in density. Unfortunately, experience 
has shown in some cases that this decrease would scarcely cease 
until the freeboard had approached vanishing point; and thus, 
for the sake of the safety of ships, cargoes, and lives, it has been 
absolutely necessary to fix upon standard types of vessels adapted 
to certain freeboards, which, as a rule, are most willingly 
accepted by shipowners, and, indeed, in some cases, more free- 
board is given to vessels by the owners themselves than even 
the Board of Trade rules demand. 

The heavier the cargo, especially in ships of great length to 
depth, the greater the bending and twisting strains experienced 
when among waves, and hence the greater necessity of increased 
structural strength. 

Vessels, according to their structural strength, etc., are classified 
under different names or types, which are often heard and used, 
but less often understood. There are, again, degrees in each 
particular type ; for example, by 100 Al at Lloyd's is meant 
vessels built to the highest class of their particular type, and 
therefore fulfilling all the requirements for such class ; 95, 90, 
and 80 A are lower classes, and do not therefore fulfil the require- 
ments of the one above them. Such vessels have greater free- 
board, and therefore carry less deadweight. 

First. — The most important of these types is that known as 
the Three Deck, This is the best deadweight carrier, and there- 
fore ranks as the strongest type of vessel built. This is the type 
of vessel used in illustrating the growth of structural strength 
for size of vessel in figs. 45 to 51, and includes the smaller 
vessels requiring only one or two decks. 

Second, — A difficulty sometimes experienced in the three-deck 
type was, that partly owing to the loss of cargo space occupied by 
the shafting and enclosed by the tunnel, it was found impossible 
with some cargoes to trim the vessel by the stern, as desired, and 
hence, for part of the after length, the ship was increased about 
4 feet in depth, and became known as the Raised QuaHer Decker 
(see fig. 66). Such vessels are really parts of two different- 
vessels joined together, and each built as near as possible to the: 
previous rule for one-, two-, and three-deck vessels. 

The sizes of all floors, frames, and reverses are governed byi 



BTRUC^UBB, 



95 



Lloyd's first number to the main deck. The frames run up to 
the quarter deck, and the alternate reverse frames also. The 
number and arrangement of hold beams, beam stringei-s, and 
stringers in hold in the way of the raised quarter deck, are in 
accordance with the increased depth of the vessel at that part, 
and the height of the reverse frames is regulated by the Lloyd's 
first number, which the increased depth would give. The aim 
•is to make the raised quarter deck an integral part of the whole, 
and the result is that a great amount of extra strengthening has 
to be introduced at the weakest part, which is in way of the 
break, by overlapping the decks and stringers, doubling the 
sheerstrake, and fitting webs between the overlapping part of 
the two decks, 'So as to better bind the structure together (see 
A, fig. 66). As the three-deck and the raised quarter-deck 
vessels are types which secure least freeboard, it is usual and 



1 



Ti 



1 




BRiooe 0* 




OIAPHRACM 
\ PLATeS 

i MAIN 0« 



T 



F 



A 

Fig. 66. — Raised Quarteii Decker. 



I ^^b^koLb^ 



certainly of great value to erect a bridge over the engines and 
boilers, and thus protect this most important part from the inroad 
of the sea. In addition to this, for the accommodation of the 
crew and passengers, a forecastle or poop is often erected, which, 
according to their respective values of affording additional effective 
buoyancy, may further be a means of reducing the freeboard 
(see chapter on "Freeboard"). 

TJiird, — When a vessel is required to carry cargoes of lighter 
density, it is usual to adopt the Spar-Deck type^ as these vessels, 
while possessing the same interior cubical capacity as the three 
deck, are of lighter construction, and have greater freeboard. 

Fourth, — Where the 'tween decks is required for passengers, 
or to carry very light cargoes of great bulk, the Awning-Deck 
type is usually chosen, as the awning deck is simply a light, 
entirely-closed superstructure over the main deck. Being of 
lighter construction, she is less capable than either the three- 



96 KNOW YOUR OWN SHIP. 

decker or the spar-decker for carrying deadweight, and therefore 
has the greatest freeboard. 

Perhaps the simplest way of comparing the structure of these 
types of vessels will be by referring to a midship section of each 
of them. 

Let figs. 67, 68, and 69 be midship sections of three vessels 
identical in their exterior appearance, each being 260 feet long, 
35 feet beam, and 24 feet depth to the uppermost deck at the 
side from the top of the keel. Fig. 67 is the midship section of 
the three-decked type. 

Fig. 63 is the midship section of the spar-deck type, the spar 
deck being the uppermost deck, and 7 feet above the main deck. 

Fig. 69 is the midship section of the awning-deck type, the 
awning deck also being the uppermost deck, and 7 feet above the 
main deck. 

We have already observed that Lloyd's first number governs 
the sizes of all the frames, reverse frames, floors, bulkheads, and 
pillars, and that the depth of one-, two-, and three-decked vessels 
is taken to the uppermost deck. In the case of spar-and awn- 
ing-decked vessels, the depth and girth are only taken to the 
main deck, with the result that the first number for these 
vessels is considerably reduced, hence the difference in the sizes 
or scantlings of the frames, reverses, floors, bulkheads, and pillars 
(compare respective sections). Then, with a reduced first number, 
follows a reduced second number, governing the sizes of the 
outside plating, keelsons, stringers, etc. 

Thus far the spar- and awning-decked vessels are identical, 
so we must note the distinction. 

Spar-Decked vessels, according to Lloyd's, are supposed to have 
three tiers of beams; and to be not less than 17 feet depth from 
the top of the keel to the main deck. Should the depth be less 
than this, a modification must be made in the freeboard assigned. 
In all cases the frames extend from the keel to the gunwale ; 
the reverse frames extend to the main and spar decks alter- 
nately ; a thick sheerstrake is fitted to both the main and spar 
decks; the side plating above the main-deck sheerstrake is less 
in thickness than that below; the main and spar decks, when 
of wood, are each Z^ inches thick, laid and caulked ; spar deck 
beams, stringer and tie plates are lighter than those required for 
the upper deck of three-decked vessels. Since the depth is only 
taken to the main deck, and the strength above the main deck is 
considerable, greatly increasing the efficiency of the ship girder 
in resisting longitudinal strains, they do not require any addi- 
tional strengthening for extreme proportions until over 13 depths 
to length, while in the three-deck type over 11 depths to upper 



STRUCTURE. 97 

deck in length is considered an extreme proportion, thereby 
requiring additional strengthening. 

In Awning-Decked vessels all frames extend to the awning deck ; 
the reverse frames extend to the main deck ; the side plating above 
the main deck is greatly reduced, and no sheer-strake is fitted to 
the awning-deck ; awning-deck beams are lighter than those 
required for spar- decked vessels. Since the awning-deck is simply 
a light superstructure, it is necessary that these vessels have a 
complete main deck laid and caulked. These vessels are considered 
of extreme proportions when over 1 1 depths to length, the depth 
being taken to the main deck. 

The reader will be greatly aided in grasping these differences 
by comparing the sections. 

Bulkheads. — Watertight bulkheads are iron or steel divisions 
arranged either transversely or longitudinally, dividing the vessel 
into watertight compartments. They also give strength, but their 
chief function is to afford safety, so that, should any compartment 
by any chance or accident be flooded, it is intended that the 
vessel will still float in comparative safety. Most of the large 
liners and warships built in these days are divided and sub-divided 
into numerous watertight compartments, having bulkheads far in 
excess of the requirements of Lloyd's, or any other classification 
society. Thus it is possible in many cases for several of these 
compartments to be damaged and flooded before endangering the 
safety of the vessel. 

Screw steamers classed at Lloyd's have a bulkhead at each end 
of the engine and boiler space, and another near each end of the 
vessel. The necessity of having the engines and boilers encased 
in a watertight compartment is obvious. The foremost or col- 
lision bulkhead should be situated at not less than about half the 
midship beam of the vessel from the stem. The fore end of the 
vessel being the part most likely to be damaged in case of colli- 
sion, and the strain which comes from panting tending to make 
leakage, explains the necessity of having this end of the vessel 
watertight. At the after end of the vessel, however, though free to 
some extent from the danger at the fore end, there is severe strain, 
especially in high-speed vessels, due to the vibration of the shaft- 
ing. As the danger is that the aft end shell plate rivets may be 
worked loose and leakage occur, this part also is made watertight. 

Though in short vessels it may be quite possible for one of these 
five watertight compartments to be flooded, and the vessel to 
remain afloat, it will be evident that in long vessels the lengths of 
the fore- and after-holds would be so great that were one of them 
damaged, and the sea to enter, the loss of buoyancy or floating 
power would be so great that sinking would be inevitable. 

G 



98 



KNOW YOUR OWN SHIP. 




uo 



Three- Deck Type— 10*4 depths to upper deck in length. 

14-5 '.. middle 



)» 



» 



Fig. 67. — Midship Section of a Thkke-Decked Type or Vessel, 



STRUCTURE. 



99 



Lloyd's Numerals. 



i Girth, . 
I Breadth, 
Depth, . 



1st No., , 
Length, . 

2nd No., 



39 1 
17-5 
24-78 

81-33 

7 

74-33 
258 

19177 



8 — 7 
Frames, 5 x 3 x ~, spaced 24 inches. 

20 
Reverse frames, 3 x 3 x ^. 

Floors, 23i X ^ ~ ^ 



20 
Centre keelson, 22^ x 



13 - 11 
"20~" 



Keelson continuous angles, 5^ x 4 x ^. 

Intercostal keelson plate, ^. 

Upper deck beams, 7i x^^, bulb plate with 1 ^ ^^ ^ 

Double angles, 3 x 3 x ^ j •' 

Middle deck beams, SJ x ^^, bulb plate with \ ^nd frame 

Double angles, 3 x 3 x A J ^ ^ 

Hold beams, QJ x ^ \ , q. , - 

Double angles, 4 x 4 x ^ /^^ ^^^^^ ^^^^ *'^*°^®- 

Upper deck stringer plate, 62 x ^ - 31 x ^. 

Middle deck stringer plate, 52 x ^^ - 31 x ^. 

Hold stringer plate, 34 x ^ - 26 x ^. 

Gunwale angle bar, 4J x 4^ x 2®^. 

Sheer strake, 42 x ^^ ~ ^^ 



Garboard strake, 36 x 



20 
12 - 11 

20 



Keel, 9^ x 2^. 

Hold pillars, 3|. 

Upper deck, 4 inches thick, laid and caulked. 

Miadle deck, 3} inches thick, laid and caulked. 

Additions for Extreme Length, 

Centre keelson increased in depth. 

To side keelson, a bulb is added for J L amidships. 

To bilge keelson, a bulb is added for | L amidships. 

To bilge stringer, an intercostal plate is added for J L amidships. 



100 



KNOW YOUR OWN SHIP. 



. ^"'' 'TMII III limga; 



rT 




SMECR STRAKC 



SMECII STRAKC 



tta 

20 



tOS 




Spar-Deck Type— 14§-2=12i depths in leiigtli. 

Fig. 68.— Midship Section of a Spar-Dfxked Vessei,. 



STRUCTURE. 101 



Lloyd's Numerals. 

i Girth, 32-1 

I Breadth, 17*5 

Depth 17*73 

1st No., 67*33 

Length, ....... 258 

2nd No., 17371 



7 — fi 
Frames, 4 x 3 x , spaced 23 inches. 

Reverse frames, 3 x 3 x ^V 

Floors, 20i X ?-^. 

20 

Centre keelson, 17 x — ~ . 

20 

Keelson continuous angles, 5 x 4 x ^^y. 

Intercostal keelson plate, ^7. 

* Complete steel deck, ^, 

Spar-deck beams, 7 x Z^, bulb plate with ) ^nd frame 

Double angles, 3 x 3 x ^ j °" ®^®^y ^^^ ^^^^^' 

8 — 7 
Main deck beams, 6 x 3 x , bulb angle on every frame. 

Hold beams, 9i x ^%, bulb plate with \ , q., . 

Double angles, 4 x 4 x ^ /°^ ®^®^y ^^^^ "^*°^®* 

Spar-deck stringer plate, 44 x .^ - 29 x ^^5. 
Main deck stringer plate, 37 x ^^ - 29 x ^. 
Hold stringer plate, 32 x ^\ - 25 x ^%. 
Gunwale angle bar, 4 x 4 x -^jf, 

Garboard strake, 36 x ^-^-1". 

' 20 

Keel, 9 x 2^. 

Hold pillars, 3. 

Spar-deck, 3^ inches thick, laid and caulked. 

Additions for JExtreme Length, 

To thickness of sheer strake, ^ is added for f L amidships. 
To strake below sheer strake, ^ is added for J L amidships. 
To bil^e keelson, a bulb plate is added for ^ L amidships. 
To thickness of 2 strakes at bilge, -gV is added for ^ L amidships. 

* Taking out the scantlings of this spar-decked vessel according to her numerals and 
proportions, a steel deck is required, as shown upon the Midship Section. But Lloyd's 
rules say : " In no case will the material at the upper part and the nim[iber and thick- 
ness of steel or iron decks be required to be greater than that of the three-decked 
vessel of the same dimensions." However, as a spar-deck vessel must have a complete 
main deck laid and caulked, though it may be of wood 3^ inches in thickness, a common 
practice among shipowners of choosing a steel deck has been followed in this Midship 
Section. 



102 



KKOW YOUR OWN SHIP. 




8-. - 



* ■ SMCCR STRAKE 
AND OOUSUNG 



tu-9_ 
20 



to d 

20 



20 



STRAKE 
OOUBLCD 



AwniDg-Deck Type— 14*6 depths in length. 
Fig. 69. — Midship Section of an Awning-Decked Vessel 



STRUCTURE. 



103 



Lloyd's Numerals. 

i Girth, 32-1 

i Breadth, 17*5 

Depth, 1773 

IstNo., . . . . . . 67-33 

Length, 258 

2nd No., 17371 

7 — 6 
Frames, 4 x 3 x i — -— , spaced 23 inches. 

Reverse frames, 3 x 3 x ■^. 

Floors, 20i X ^-Zl. 
* ^ 20 

J* 

Centre keelson, 17 x — ^~- , 

Keelson continuous angles, 5 x 4 x ^\. 

Intercostal keelson plate, ^f^. 

Complete steel deck, ^. 

Awnmg-deck beams, 6| x 3 x ^%, bulb angle on alternate frames. 

8 — 7 
Main deck beams, 6 x 3 x — ^.- , bulb angle on every frame. 

Hold beams, 9i x ^, with \ .q., . 

Double angles, 4 x 4 x ^«^ /°'^ ®^®^ ^^^^ "*™®- 
Awnin^-deck stringer plate, 32 x ^^. 
Main deck stringer plate, 37 x ^^ - 29 x ^f^. 
Hold stringer plate, 32 x ^p^ - 25 x ^f^. 
Gunwale angle bar, 4 x 4 x ^^. 

Garboard strake, 36 x 1L~J_^. 

' 20 

Keel, 9 X 2|. 

Hold pillars, 3. 

Awning-deck, 3 inches thick, laid and caulked. 

Additions for Extreme Length, 

Sheer strake, doubled whole width below stringer plate, for f L amidships. 
To upper deck stringer, ^ is added for J L amidships. 
One strake at bilge, doubled for ^ L amidships. 



104 



KNOW YOUR OWN SHIP. 



Lloyd's, therefore, require that in vessels 280 feet and over in 
length, an additional bulkhead be fitted in the main hold; and 
when over 330 feet in length, another bulkhead be placed in the 
after-hold. 

All bulkheads should extend sufficiently high, so that in the 
event of any compartment being flooded, there would not be the 
danger of the water pouring over the top of any bulkhead. The 
collision bulkhead should extend to the height of the uppermost 



.INER 



0) 

u 

z 

u. 

u 

J 
o 

o 

o 





Elevatiou of bulkhead. 



Ii.teraal view of ship, shcwiug'ccnnectioii of 
bulkhead to shell. 



BULKHEAD 




SH^LL PLATING 

B Plan 

Fig, 70. — Connection of Bulkhead to Shell. 

deck, and its watertightness tested by filling the foremost compart- 
ment with water to the height of the load waterline. 

The bulkhead bounding the engine and boiler space should 
extend to the upper deck in one-, two-, and three-deck vessels; to 
the spar-deck in spar-decked vessels ; to the main deck in awning- 
decked vessels. 

The aftermost bulkhead should extend to the upper deck, or to 
the spar-deck, and should also be tested to ensure watertightness 
by filling the after peak to the load waterline. 



STRUCTURE. 105 

Should the vessel be long enough to require other bulkheads, 
they should extend to the upper deck in one-, two-, and three-deck 
vessels ; to the spar-deck in spar>decked vessels ; and to the main 
deck in awning-decked vessels. 

The bulkhead plating is attached to the shell of the vessel by 
double frames (fig. 70). 

It often occurs that it is not convenient to carry a bulkhead 
continuously from the keel to its required height, but it is 
recessed or stepped in the form of a plated flat at an intermediate 
part, and then continued to its prescribed height. (See A, fig. 
71.) However, the watertightness must be maintained. This 
may be done by cutting the reverse frames and fitting angle 
collars round the frames in way of the flat, as shown by B, in fig. 
71, or cast-iron chocks between the frames (C, in fig. 71), or else 
the frames may be cut, and the flat connected to the shell by a 
continuous angle, with brackets above and below joining the flat 
to the frames (D, in fig. 71). When a bulkhead is stepped on a 
water ballast tank it should be connected by double angles, or in 
the case where it terminates at a deck, or is fitted in a 'tween 
decks, it should be attached to the decks by double angles. 
Where a bulkhead extends above an iron deck, the longitudinal 
strength is preserved by keeping the deck continuous, and stopping 
the bulkhead at the under side, then continuing it again above 
the deck, making the connection by double angles. In fitting 
iron collars in w^ay of a watertight flat, the reverse frame is cut 
and the main frame doubled for about three feet to compensate 
for the break in the reverse frame. Being very expensive, this 
method is not often adopted. When cast-metal choeks are fitted 
they are first bedded in cement, and a space of about three- 
quarters of an inch left all round. This space is filled with metal 
filings — the waste from drilling machines — which, when rusted 
and caulked, forms very satisfactory watertight work. The edges 
and butt laps in all bulkheads must be caulked. This is necessary 
on one side only. It is better to caulk the collision bulkhead on 
the after side, and the aftermost bulkhead on the fore side. One 
reason for this is that it is more easily done ; but the chief one is, 
that when these peaks are tested by a head of water, should leak- 
age take place, the exact spot is easily perceived and caulked. 
For the other bulkheads, it is of little consequence on which side 
they are caulked. 

It is always better to avoid any abruptness in longitudinal 
strength, and thus all keelsons and stringers should be continuous 
through bulkheads. This necessitates making the bulkheads 
watertight at these places by fitting angle collars on one side of 
the bulkhead, and often plate collars on the other. The angle 



106 



KNOW YOUR OWN Sfil^. 



V 




FLAT 



CNLARCCO View OF ONC FRAMCSPACC AT C 




SECTION 
THROUGH 

c 



WATERTIGHT 
FLAT 



P=\lr-iJj-i1' 



Fig. 71. — Recessed Bulkhead and Watertight Flat. 



STRUCTURE. 



107 




collar is fitted on the side on which the bulkhead is caulked, and 
is itself caulked (see fig. 72). 

As has already been pointed out, if any part of the vessel is 
subject to any weakening, compensation must be made in some 
form or other to recover the strength. It will be noticed that in 
attaching bulkheads to the shell plating, a double row^ of holes has 
to be pimched, one of which is spaced 4 to 4J diameters apart. 
The result is that the shell plating round the whole girth of the 
vessel has been greatly weakened. Compensa- 
tion is made for this by fitting what are called 
liners in the way of all outside strakes, where 
practicable. These are plates extending, as 
shown in A, fig. 70, for at least two frame 
spaces from the toe of one frame to the heel 
of another, and from the edges of the two 
inside strakes adjacent. The riveting in 
bulkhead liners is arranged where convenient. 

Longitudinal bulkheads continuous all fore 
and aft in twin-screw vessels also provide a 
means of subdivision, but at the same time they 
may afford great longitudinal strength if well 
constructed and stiffened, especially in very 
long vessels, and more particularly so in long, 
shadow vessels of the light draught type. 
Their value in stiffening ships has been proved in cases where, 
before they were fitted, the vessels suffered greatly from vibration 
from the machinery, but after they were fitted the vibration was 
greatly reduced. The reason of this is explained by our girder 
illustration. The ship, being a hollow^ girder, has its upper and 
lower flanges (decks and bottom) the more effectively united, and 
by this means the whole structure acts more in unison in resisting 
either local or general strain. 

All bulkheads must be thoroughly stiffened if they are to be of 
any service. To simply fit the sheet of comparatively thin plating 
of which bulkheads are made, from side to side of the vessel, would 
be useless in resisting any severe pressure. Bulkhead stiffening 
is composed of angle bars of the size of the main frames of the 
vessel placed vertically on one side, 30 inches apart, and on the 
other side, horizontally, 48 inches apart. According to the 
dimensions of the bulkhead, additional stiffening may be fitted in 
the form of semi-box beams, web plates, and bulb angles. In all 
cases the collision bulkhead should be additionally stiffened, since 
this is most liable to danger. 

Elspecially in the case of passenger vessels and yachts, it is often 
found necessary to have a means of passage through a watertight 



Fig. 72. — Angle 
Collars mak- 
ing Bulkhead 
Waterti ght 
ROUND Keel- 
son. 



108 



KNOW Your own ship. 



bulkhead, in order to get from one part of the accommodation 
to another. This is done by fitting iron doors, which can be 
closed and secured so as to make the bulkhead perfectly water- 



(TTTrTTT) 
^ — -fz — 



r 



n 



i?.^j 



® 



(7TTTTTT) 



;t.'4> 



(TTT?T7T) 



=^ 



.V 







S 




SECTION 



WKOCK 




PLAN 




INDIA -RUBBtK 



STEEL WEDGE 




STEEL WEDCe 

s 



INDIA- RUDDER 



Eulai'ged sketches showing two different methods of making doors watertight. 
Fic. 73. — Bulkhead Watertight Door. 



tight (fig. 73). When such a door is absolutely necessary, it 
must be provided, but whenever possible it should be dispensed 
with, for in case of accident it is very often found that the 
numerous watertight compartments into which the vessel has 



STRUCTURE. 



109 



o o 

o o 
o o 



o o 



o o 
o o 




^ 



BUTT STRAP 



Fig. 74. — Butt Strap. 



probably been divided in order to secure safety under the most 
exceptional circumstances, are rendered worthless, and sometimes 
a source of danger by these doors being left open, and either 
forgotten or unapproachable in the hour of need. 

Riveting. — A most important consideration in the production 
of an efficient vessel is good workmanship, and the greatest 
attention should be paid to sound riveting and accurate fitting of 
butt straps, etc. (fig. 74). Blind or unfair holes are often the 
result of carelessness on 
the part of workmen in 
marking off the spacing, 
or in punching the rivet 
holes. Where such occur, 
however, the drift punch 
should be strictly for- 
bidden, as its use not only 
tears and weakens the plate 
by the severity of its action, 
but to get thoroughly 
watertight work is rendered most difficult, as the rivet cannot 
fill up the cavities made in so damaging the plate. The drift 
punch is a tool, as shown in fig. 75, circular in section, which is 
driven into the hole, and a space 
for the rivet torn through. 

The proper method, when such 
holes do occur, is to rime them with 
a tool (fig. 75), which cuts away 
any projecting material and leaves 
a clean hole for the rivet. 

After a rivet has cooled down, 
and is found to be slack, or that 
the head has been badly laid up, 
or that, on testing, leakage takes 
place, the rivet or rivets should 
not be caulked to ensure water- 
tightness, as is sometimes done, but taken out and re-riveted. 

Were it not for the additional cost, it would be better to rime 
out punched holes before riveting, as this would not only clear 
the rivet holes, but to some extent restore the strength of the 
plate, which is weakened by the severity of the action of punching. 
Though much more costly, by far better work is obtained by 
drilling rivet holes, as this process not only gives fairer holes, but 
does not by its action weaken the plate. 

In punching rivet holes in plates or angle bars, the holes are 
always punched from the faying surfaces — that is, from the sur- 



o 



DRIFT 
PUNCH 



m 

w 



RIMER 



Fig. 75.— Drift Punch 
AND Rimer. 



110 



KNOW YOUR OWN SHIP. 



faces which are to lie against each other. By this means the 
plates fit hard up to each other, as a rag edge is made on the 
Outer surface of the plate in punching. 

Thus in the plates in A, fig. 76, the holes are punched in the 
direction shown by the arrows. In machine punching, the rivet 
holes gradually increase in diameter in the direction in which the 
punch passes, as shown. 

A few forms of riveting may here be taken with advantage. 
For watertight work, where one surface of the plating has to be 
flush, the pan head rivet is undoubtedly one of the best. Its form 
is as shown in B, fig. 7fi. 

It will be observed that the neck of the rivet is expanded under 



L 



I 



X 





C D E 

Fio. 76.— Mode of punching Rivet Holes, and Forms of Rivets. 



the pan head ; this, when heated and hammered, completely fills 
up the hole in plate a. In plate h^ after the rivet hole has been 
punched, it is drilled by a machine into a more conical form, as 
shown. This is called countersinking. When the rivet head is 
thoroughly beaten up, it is cut off in a rounded form, leaving it 
rather full on the flush surface of the plate. In cooling, the rivet 
contracts, and this further tends to effectually close up the hole. 
Another form of rivet is shown in C, fig. 76. The further this 
rivet is driven into the hole the tighter it wedges itself, and, if 
well hammered and laid up, it produces good results. It is still 
further improved if the work is not prominently visible, by laying 
up a point as shown in D, fig. 76, producing greater holding 
power. This also applies to the pan head rivet, which, as has 
been proved by experience and experiment, is then the most 
efficient rivet. 



8TBUCTURB. Ill 

For the sake of their better appearance, the snap head form of 
rivet has been considerably adopted in many parts of the structure 
exposed to view, especially in bulkheads. But hand-riveted snap 
head rivets have not produced satisfactory results. In clenching 
up the point of the rivet with the tool called the snap cup^ the 
effect is to bring the edges of the rivet close, in the form of a point, 
as shown in E, fig. 76, leaving a hollow all round under the head 
of the rivet. 

So long as the rivet is kept dry it works weU enough, but when 
water gets to it the pointed edge rusts, and corrosion is set up in 
the plate also, with the result that, after a time, the rivet works 
loose, and, in many cases, they can be twisted round by the fingers. 

Where the work has to be strictly watertight, a far better result 
is secured by simply hammering the point down hard on the plate, 
though the appearance is certainly not so taking. Nevertheless, 
appearance should be sacrificed, rather than efiiciency and 
strength. 

Where snap riveting is performed by a machine, however, the 
results are very satisfactory, since the machine has the power of 
more effectually clenching up the point of the rivet. But it is 
only in some parts of the structure where machine riveting can 
be carried out, although in every case it is superior to hand 
riveting. 



112 KNOW YOUR OWN SHIP. 



CHAPTER VI. (Section I.) 
STABILITY. 

Contents. — Definition — The Righting Lever — The Metacentre — Righting 
Moment of Stability — Conditions of Equilibrium — ** Stiff" and 
"Tender" — Metacentric Stability — Moment of Inertia — Agents in 
Design influencing Metacentric Height — How to obtain Stiffness — 
Changes in Metacentric Height during the Operation of Loading — 
Stability of Objects of Cylindrical Form — A Curve of Stability — 
Metacentre Curves — How the Ship's Officer can determine the Meta- 
centric Height and then the position of the Centre of Gravity in any 
condition of Loading — Effect of Beam, Freeboard, Height of Centre 
of Gravity above top of Keel, and Metacentric Height, upon Stability 
— "Wedges of Immersion and Emersion — Effect of Tumble Home upon 
Stability — Stability in Different Types of Vessels. 

Definition. — By the term stability la meant the moment of 
force (usually measured in foot-tons, or in inch-tons), by means 
of which a vessel, when inclined out of the upright position 
through some external force, immediately endeavours to right 
herself. Stability is dependent upon design and loading. 
Many ocean-going craft have not sufficient stability to stand 
upright when light, and loll over, and some will not stand at 
all in this condition without ballast. But ships are not built to 
sail upon the open sea light, and these same vessels may be so 
regulated in the operation of loading as to be changed into 
splendid sea boats. 

The Righting Lever. — In Chapter II. we explained the 
meaning of a foot-ton — viz., that 1 ton of force multiplied by a 
leverage of 1 foot equals 1 foot-ton. Now, if we say that a 
vessel of 1000 tons displacement has a righting moment of 
stability of 2000 foot-tons when inclined to an angle of, say, 30', 
we mean that the weight, 1000 tons, is acting at a leverage of 
2 feet, since 1000 x 2 = 2000 foot-tons ; and this is the 
righting tendency possessed by this ship when inclined to an 
angle of 30**. The two factors in the moment of stability are 
weight and leverage. The weight is always the total displace- 
ment. 

The leverage we shall now endeavour to explain. 



StABliilTY. 



113 



Fig. 77 represents two midship sections of the same vessel, one 
floating upright and the other inclined to an angle of about 14**. 
When she floated in the upright condition, W L was the water- 
line ; the point B is, at the same time, the centre of buoyancy or 
centre of gravity of the water displaced by the ship, and G is, for 
that -kind of loading, the centre of gravity of the ship and her 
loading. But when the vessel became inclined, as in the sketch, 
she floated at the waterline W L'. Observe what has happened. 
The displacement has certainly changed in form, but not in total 
volume or weight ; that remains exactly the same, because the 
weight of the ship and the cargo remain exactly the same. But 
the centre of buoyancy has moved towards the right to B', which 
is the new centre of displacement (that is to say, the new centre 
of the water displaced by the heeled ship), the old B being no 



-^ 




Fig. 77. — Vessel floating Upbight, and Inclined 14''. 



longer that centre. The centre of gravity of the ship and its 
loading, G, remains in the same position in the ship as before, 
whatever be the angle of heel, so long as we do not alter the 
loading. It must always be the centre of weight, and will never 
move, as just stated, so long as the weights on board remain 
stationary. The weight of the ship, like all weights, acts 
vertically downward through its centre of gravity, G, and the 
pressures of buoyancy act vertically upward through the centre 
of buoyancy, B or B', as the case may be. When the ship was 
upright, the two points were in the same vertical line, but after 
being inclined, their forces acted through their centres in the 
direction of the arrows on tKeir vertical lines of action, leaving 
a horizontal distance between them, because, now they are not in 
the same vertical line. This perpendicular — that is to say, 
horizontal — distance between the two vertical lines of action, 
gives the lever, GZ; and this very important distance, GZ, is 



114 KNOW YOUR OWN SHIP. 

the lever we want, and which we mentioned previously as one 
of the factors in the measure of a vessel's stability. 

The Metacentre. — It will be noticed that the vertical line 
through the centre of buoyancy intersects the centre line of the 
section of the vessel at the point M. This point is called the 
metacentre^ and is always at the intersection of these two lines, 
which is approximately a fixed point up to angles of about 12** 
or 15** of heel for ship-shaped objects. Usually, at greater 
angles, the vertical line through the new B' no longer intersects 
the centre line of the ship at the point M. 

Righting Moment of Stsi-bility. — When M is above G, the 
lever is properly termed a righting leveVy for then the action of the 
buoyancy is to push the vessel again into the upright position, as 
can easily be seen in fig. 77. When M is below G, the tendency 
is to add to the inclining force, and in this case the lever is an up- 
setting one. In the sketch, it is evident that the lever is a 
righting one, and therefore the displacement of the vessel multi- 
plied by this leverage measured in feet, say, at any particular 
angle of heel, gives the righting moment of stability in foot-tons 
for that angle. 

Conditions of Equilibrium. — So long as there is a leverage, 
the vessel, if left free to move, will not remain at rest, or, as it is 
generally termed, in a state of equilibrium ; and the longer the 
leverage, the greater is the moment tending to bring her back to 
the upright condition, or to capsize her, as the case may be ; and 
the longer the righting lever up to angles of 12° or 15° in 
ordinary vessels, the higher must the metacentre be above the 
centre of gravity. Thus, for a vessel to float upright in a state 
of equilibrium or rest, it is evident that the centre of buoyancy 
and the centre of gravity must be in the same vertical line, the 
force of gravity of the ship and buoyancy of the water neutral- 
ising each other. But it dues not follow that in this condition 
the equilibrium will be stable. For if, under the effect of some 
external force (such as wind), the vessel heel, and the metacentre, 
before heeling, be below the centre of gravity, the result will be 
to push the vessel further over, not necessarily by any means to 
capsize her, but (it may be) to a position such as to cause the 
upward vertical line of action of the buoyancy to coincide with 
the downward line of action of the weighty when the vessel will 
again remain at rest. When the vessel floated upright before 
the inclination took place, she might have been compared to a 
child's play top carefully balanced upon the point, a condition 
it would not be likely to remain in for a long period. This 
equilibrium is called unstable equilibrium. When the meta- 
centre is above the centre of gravity, and thus, under the least 



• 



STABILITY. 115 

inclination, the vessel immediately endeavours to regain the 
upright condition, the equilibrium is termed stable equilibrium. 

"Stiff" and "Tender." — When the metacentre is high 
(equivalent to large righting leverage), and the righting moment, 
when the vessel is inclined, is therefore great, the vessel is said 
to be " stiff,^^ and when the metacentre is closer to the centre of 
gravity, and the vessel naturally possesses small righting leverage 
for small angles of inclination, she is said to be "craw/<;," or, as 
sailors more commonly say, "^e/icZer." 

When the centre of gravity and the metacentre coincide — that 
is, when both j)oints occupy the same position, — the equilibrium 
is then neutral, neither stable nor unstable. 

Metacentric Stability. — Having foimd the distance between 
the metacentre and the centre of gravity, the actual lever of 
stability may be found for small angles of heel not exceeding 
15', by multiplying this distance by the sine of the angle of 
heel (using natural sines*).. Then leverage in feet multiplied 
by displacement in tons equals righting moment in foot-tons. 
This stability, which is deduced from the metacentric lieiglif, 
or, distance from M to G in fig. 77, is termed metacentric 
stability. 

Our next endeavour must be to discover the position of these 
points, and to ascertain how they are influenced. The centre of 
buoyancy we have already studied in Chapter III., and have 
found its position to be always in the centre of displacement, 
and also, when the vessel is floating upright, that it is always 
a fixed point at any particular waterline. 

The metacentre also is a fixed point for each successive draught 
when the vessel floats upright, and thus, by calculating a few of 
these points, a curve may be constructed, thereby enabling the 
position of the metacentre to be ascertained at any draught. 

But, first of all, let us see how the design or dimensions of a 
vessel affect the position of the metacentre. The formula for 
finding the metacentre is : — 

Moment of inertia of waterplane _ / Height of metacentre above centre of 
Displacement in cubic feet I buoyancy. 

To give the usual definition of Moment of Ineiiia would prob- 
ably be to sound the keynote of despair to many a seaman. 
A simple, though perhaps not very scientific method may be 
used, reducing this to terms sufficiently plain to be understood 
by seamen with the most limited mathematical knowledge. 

* See table of natural sines at end of book. Such a table is printed in 
many books on Navigation, 



116 KNOW YOUR OWN SHIP. 

Moment of inertia may be understood as the measure of the 
tendency possessed by the superficial area of the waterplane of 
any floating object, to remain inert, dead still, or motionless. It 
must be clearly understood that this moment of inertia applies 
only to the waterplane area at which the vessel is floating, whether 
the vessel be a ship, a box, or a log of wood. Thus, the fact that 
there may be one part of the floating object out of the water, and 
another part in it, is left entirely out of consideration. Simply 
area at the waterline is dealt with. The formula for moment of 
inertia of a rectangular-shaped waterplane is as follows : — 

Cube the side at right angles to the longitudinal axis, multiply 
this by tJie length of tJie waterline, and divide the result by 12. 

Note, — All measurements should be in feet to match the displacement. 







-y- 




LoMCiTUDiNAu Axis 


1 




^ 50 >^ 

\ 1 


Li-- 



Fig. 78.— Plan of Waterplane. 

For example, take ^g, 78, which is a plan of the waterplane of 
a box-shaped vessel 50 feet long, 10 feet broad, and 8 feet draught. 
The moment of inertia would be : — 

102_x^ = 10 X 10 X 10 X 50 ^ 4igg.gg ^^^3^^ ^f .^^^^.^ 
12 12 

The student should note that since the dimensions and area 
of all the waterplanes of a box-shaped vessel, floating with the 
bottom parallel to the waterline, are equal to one another, the 
moment of inertia of each waterplane is the same. 

But let us proceed to find the height of the metacentre. This 
is done by dividing 4166*66 by the displacement in cubic feet; 
the result is the height of the metacentre above the centre of 
buoyancy. The draught is 8 feet. It is, therefore, evident that 
the object, being of box form, the centre of buoyancy must be at 
half the draught, which is 4 feet above the bottom. The dis- 
placement in cubic feet will be the volume of the part of the 
vessel immersed, which equals : — 

50 feet length x 10 feet breadth x 8 feet draught = 4000 cubic feet 

displacement. 

Then ~ " . = i '04 feet height of metacentre above centre of buoyancvr 
4000 ^ 



STABILITY. 117 

Now, the question may be well asked at this stage — Of what 
value is this result? The only answer is, that these points, by 
themselves, are of no practical use, and give no idea whatever of 
a vessel's stability, until we get the position of the centre of 
gravity. Let us suppose the height of the centre of gravity from 
the bottom of the box to be 3 feet (the box having, of course, a 
load in its lower part, so as to keep the centre of gravity of the 
loaded box down to 3 feet). 

Since the metacentre is 1*04 + 4 = 5*04 feet from the bottom 
of the box, therefore the distance of the centre of gravity below 
the metacentre is 5*04 - 3 = 2*04 feet, proving that the vessel 
is floating in a condition of stable equilibrium. While floating 
at this • draught, imagine a weight of 20 tons already on board 
to be raised 13 feet. Observe distinctly the new state of afiairs, 
supposing that after the alteration the vessel floats upright. 
The displacement, the positions of the centre of buoyancy and 
metacentre are all just the same as previously, no alteration 
having occurred in the draught. There has, however, been a 
change in the position of the centre of gravity, thereby affecting 
the distance between the changed centre of gravity and the 
unchanged metacentre. Any vertical movement of weight in 
the box must either raise or lower the centre of gravity, con- 
sequently, in the case before us, since the weight of 20 tons was 
raised, it follows that the centre of gravity must have travelled 
in the direction of the shifted weight. But how far? We 
have already discovered how to find this in the chapter on 
" Moments," viz. : — 

Multiply the weight by the distance it has been maved, and divide 
hj tlie total displacement (4000 cubic feet = 114*2 tons), 

20 X 13 ^ o .o feet = i Distance centre of gravity 
114-2 t has moved upwards. 

We now see that the centre of gravity, instead of being below 
the metacentre as previously, has risen to (2*2 - 2*04) = 0*16 of 
a foot above it. If the box remain upright, it is in a condition of 
unstable equilibrium, and any exterior force upon it will readily 
cause it to heel. As the vessel has not sufficient stability to 
float upright, the vital question is — Will she capsize? In the 
example before us, the vessel having a good freeboard of about 
5 feet, the answer is "no," for, after inclining to an angle of 
about 18", she would remain at rest with this permanent list. 
Let us again investigate the circumstances. The centre of 
gravity has remained stationary imder the inclination. We 
observe a slight movement of the centre of buoyancy from its 



118 KNOW YOUR OWN SHIP. 

old position to the new centre of displacement. In the earlier 
stage of this inclining movement, the vertical line through the 
centre of buoyancy intersected the centre line of the vessel below 
the centre of gravity, in fact, as always for very small heels, at the 
metacentre, making a leverage between the vertical lines through 
the centre of buoyancy and the centre of gravity. This point 
of intersection being below the centre of gravity, the heeling 
continues, for the moment is an upsetting one, the buoyancy 
expending itself in pushing the vessel further over. Reference to 
Hgs. 16 and 77 will assist in tracing the movements of these points. 
However, after inclining to an angle of about 18°, it would be 
found that the centre of buoyancy had travelled so far out 
towards the inclining side as to bring it vertically beneath the 
centre of gravity, the vertical lines of action through these two 
points coinciding. The upsetting lever having vanished, the 
box floats in a condition of equilibrium, having neither righting 
nor capsizing moment, and will move neither towards the port 
nor the starboard except by the application of sheer exterior 
force. For vessels of cylindrical form, and, therefore, circular 
in section, the metacentre is the point of intersection of the 
vertical line through the centre of buoyancy with the centre 
line of the cylinder /or oM angles of inclination, and, knowing this, 
we shall soon see how the whole range of such an object's stability 
may be readily determined. As we have observed, vessels of 
ship form differ from cylinders for large angles of inclination, and 
another method has to be adopted in order to trace out the 
whole range of stability. See Stability Calculation, Chap. X. 

Agents in Design Influencing Metacentric Height. — The 
two important factors in the design of a ship influencing the 
height of the metacentre are beam and displacement. The 
formula for the moment of inertia of the waterplane of a box 
vessel we have already stated as: — 

Length x Breadth^ 
12 ' 

so that, as the breadth is cubed, any addition to this dimension 
must have greater eflect in increasing the moment of inertia of 
any waterplane than a similar addition to the length. 

The formula for height of metacentre above centre of buoyancy 
is : — 

Moment of inertia of load waterplane 
Displacement 

It must, therefore, be evident that the smaller the displace- 
ment, the greater will be this height. Had the displacement of 



STABILITY., 119 

the box vessel, referred to previously, been reduced by cutting 
ojffthe bottom corners and making it more triangular in shape, 
preserving the same area of waterplane, a much higher metacentre 
would have been obtained. Thus, fine vessels with good beam 
produce the highest metacentres. These points may be more 
vividly illustrated by means of a few simple examples : — 

Let 2 feet be added to the beam of the box vessel with which we have just 
been dealing, the draught remaining the same. The dimensions will now be 
— Length, 50 feet ; breadth, 12 feet ; draught, 8 feet. 

The moment of inertia = ^^ "^ ^^ - 7200. 

12 

The displacement =» 50 x 12 x 8 =- 4800 cubic feet, 

7200 



4800 



1 '5 feet = metacentre above centre of buoyancy. 



In the original condition, the metacentre was 1*04 feet above the centre of 
buoyancy, and 2*04 feet above the centre of gravity. 

The metacentre, being raised (1*6 - 1*04 ==) 0*46 of a foot, by the addition 
of 2 feet to the beam, in its turn increases the metacentric height to 
(2*04 + 0*46 =) 2*5 feet, greatly adding to the stiffness of the vessel. 
Had we added 2 feet to the length of the vessel, certainly the moment of 
inertia would have been increased, but so would the displacement, entirely 
neutralising what might have been imagined a means of raising the meta- 
centre. 

52 X 103 ^ ^ggg.gg ^0^3^!. of mcrtia. 
12 

52 X 10 X 8 = 4160 cubic feet displacement, 

4333*33 

. ;— = 1*04 feet metacentre above centre of buoyancy, and 

4160 ^ ^ 

the same as the original height. 

If 2 feet had been added to the draught, the moment of inertia would 
have remained the same: — ^ — — = 4166*66, and the displacement would 

naturally have been enlarged, 60 x 10 x 10 = 5000 cubic feet. The evident 
result must be that in relation to the centre of buoyancy, the metacentre is 

now lowered, for ^--^^- = 83 of a foot metacentre above centre of buoyancy, 

5000 

which is less than the original 1 *04. 

By these simple illustrations it is clear thai team is the most 
important factor in the dimensions of a vessel by means of which 
a high metacentre is obtained, simply because the breadth of the 
vessel is used in the third power, while the other dimensions are 
used only in the first power, in the process of calculation. It 
will also be noticed that the position of the weights carried 



120 KNOW YOUR OWN SHIP. 

governs the position of the centre of gravity of the loaded 
vessel. 

How to Obtain StifEhess. — We have now discovered two 
means of obtaining stiffness — first, by placing heavy weights as 
low as possible, thus drawing the centre of gravity down from 
the metacentre ; and second, by adding to the beam to raise the 
metacentre. 

Changes in Metacentric Height when Loading. — We can 
also the better understand how it is that some vessels, especially 
when loaded with homogeneous cargoes, get tender when the 
last part of the cargo is being put on board, and the load water- 
line approached. For some distance below the load waterline, 
little or no increase has occurred in the area of the waterplane. 
In fact, where the vessel possesses great tumble homey* it may 
even happen that the width of the waterplane at ihe load line is 
less than at 1 or 2 feet below it, and we have seen what effect 
any reduction in the beam has upon the moment of inertia. 
Now, while with increasing load, no increase may have been 
occurring in the moment of inertia while nearing the load water- 
line, the displacement has certainly continued to increase with 
the increasing load. The metacentre and the centre of buoyancy 
have, therefore, come nearer each other. But at the same time, 
the centre of buoyancy has certainly risen above the keel some 
distance, being now the centre of a greater displacement, and 
may have risen more than the metacentre has sunk. The result 
is that the metacentre may actually be higher from the keel 
than before. But the continuation of the loading producing this 
rise in the centre of buoyancy above the keel has also raised the 
centre of gravity above the keel, with the eff'ect of reducing the 
distance between the metacentre and the centre of gravity — 
that is to say, the metacentric height is reduced, or, the vessel 
has become more tender. Before any cargo was placed on board, 
the metacentre and the centre of gravity had perhaps only 5 or 6 
inches between them. In this position, the vessel would be tender, 
not at all uncommon when light. Now, let the centre of gravity 
of the unloaded ship be at half the depth of the hold. It is clear 
that when the operation of loading commences, and as long as 
weight is being placed below the centre of gravity, the centre of 
gravity must be gradually lowering, and the vessel becomes very 
stiff in consequence, but as cargo continues to be loaded, and the 
holds are about filled, the centre of gravity rises again. It is 
also evident, that if more heavy cargo be placed above the original 

* "Tumble home " is the difference between the amidship breadth at the 
uppermost deck edge and the moulded breadth. 



STABILITY. 



121 



centre of gravity than below it, the centre of gravity must be 
higher than it was previously. We must not forget, however, 
that the metacentre has varied with every change of draught. If 
we had a curve of metacentres for the vessel, we could readily 
ascertain its correct position. If it were found that we had so 
loaded our vessel as to bring the centre of gravity again into 
proximity to the metacentre, the result would naturally be a small 
metacentric height and a tender ship. 

Stability of Cylindrical Objects. — At this stage, it will 
repay us to give a little attention to the stability of objects of 
cylindrical or cigar form, and from these simple shapes to deduce 
such principles as will help us in dealing with the more com- 
plicated ship forms. 

Let fig. 79 be such an object 50 feet long, 10 feet diameter, 
and for the sake of example, a solid piece of timber, floating half 





Figs. 79, 80, 81.— Stability of Floating Cylindrical Objects. 

immersed — that is, at 5 feet draught. The centre of gravity will 
be in the centre of the log at G. Every reader knows from 
observation that such an object will float as readily in one position 
as another, and with any of the points, a, 6, c, d^ uppermost. 
Such a condition is, therefore, one of neutral equilibrium, and this 
being the case the metacentre and the centre of gravity must 
coincide. Let us endeavour to prove this. It is clear that G is 
the centre of weight. The centre of buoyancy will be in the 
centre of the half circle in the water at B. If a piece of cardboard 
were cut to this shape, and balanced upon a point, it would be 
found to be '4244 of the half diameter of the cylinder down from 
the line CD = -4244 of 5 feet = 2*122 feet. The moment of 
inertia of the waterplaae will be 



50 X IQS 



= 4166-66, 



122 



KNOW YOUR OWN SHTP. 



The displacement is 



102 X -7854 X 50 



= 1963-5. 



A 1 dd'C fi 

Therefore, ^ — = 2*122 metacentre above centre of buoyancy, 

bringing it exactly up to G, thus proving the fact that the vessel 
floats in a condition of neutral equilibrium. 

Had the above cylinder been made of heavier wood, so as to 
float deeper, as shown in fig. 80, its equilibrium would still have 
been neutral, and in like manner the metacentre and centre of 
gravity would have coincided. 

Or again, had the object been made of lighter material, and 
floated as in fig. 81, the equilibrium would have been unchanged, 
for still the metacentre and centre of gravity would have occupied 
the one position. 

The fact to be remembered from these examples is, that tJie 
transverse metace7itre is always the centre of the circular section 
whatever he the draught. 



w 


w; 


t 




1 

1 > 


/ 




Fig. 82. — Vessel loaded with a Fixed Weight. 



But suppose the vessel is hollow, and a weight is placed inside 
and firmly fixed, with the effect of lowering the centre of gravity, 
say, 1 foot below the metacentre. The vessel floats, say, at 
half the diameter draught, 5 feet. To whatever angle the 
vessel be now heeled, the centre of buoyancy must always be in 
the centre of the immersed semicircle, and the centre of gravity 
is immovable in its position. 

When floating upright, as shown in fig. 82, the metacentre, 
centre of gravity, and centre of buoyancy are in the same vertical 
line ; but if the vessel be heeled, the centre of gravity and centre 
of buoyancy will no longer be in the same vertical line. The 
distance between the two vertical lines through the points (t 
and B' indicates the lever of stability, GZ. 




STABILITY. 123 

In heeling, it is clear that a part of the vessel of wedge shape, 
L M Z (fig. 83), formerly out of the water, is now immersed, and 
another wedge-shaped part, WKw, formerly in the water, has 
become emerged. Whenever it happens, whatever be the type of 
floating object, that the immersed wedge 
is identical in shape with the emerged 
wedge, with each of their centres the 
same distance from the vertical line 
through the centre of buoyancy, this 
vertical line will intersect at the point M, 
in the line a 6, thus keeping the distance 
from M to G (the metacentric height) 
the same. 

The lever of stability can be found 
by multiplying the distance, MG, by the 
sine of tJie particular angle of heel. This 
is true for all floating objects of cylindri- ^^^' ^^• 

cal form; and thus it matters not how 

great may be the angle of heel, it is always found that the 
immersed wedge, L M Z, is equal both in shape and volume to 
W M «?, and also that their centres, P and K (see figure), are at 
equal distances, x, from the vertical line through B'. Knowing 
this, we can proceed to ascertain the whole range* of stability for 
our cylindrical vessel. The calculations for the levers of stability 
will be made at every 10° of heel. 

A very simple method of illustrating the levers of stability for 
cylindrical vessels (and one which the reader might well try for 
himself, thereby proving by measurement the accuracy of the 
calculation) is as follows : — Cut a piece of cardboard circular in 
shape, and mark upon it in black dots the positions of the meta- 
centre, the centre of buoyancy, and the centre of gravity (1 foot 
below the metacentre) in the upright condition. Loosely attach 
the cardboard to a flat board, placed vertically by means of a 
screw through the point indicating the metacentre, so as to be 
free to revolve. Over the head of the screw loop a thin length of 
cord, and to the other end attach a button or round piece of lead, 
so as to exactly cover the centre of buoyancy. Knot another 
piece of cord, and pass it through the back of the cardboard at 
the point indicating the centre of gravity, and at an indefinite 
length hang another button or weight. When upright, the two 
cords will hang together, but immediately the cardboard diagram 
is inclined the cords will separate, and the perpendicular distance 
between them represents the lever of stability. By revolving 

* By range is meant the extent of the inclination from the upright 
position to the angle at which a ship's righting force vanishes. 



124 



KNOW YOUR OWN SHIP. 



the diagram at intervals it will be found that the levers measure 









-| 1 T I I 

0.334 






pa 
< 

ft* 
O 



> 
Pi 

o 



00 

O 



according to the calculation G M x sine of angle of heel = lever 
of stability. [Nofe.—G M = 1 foot.] 



STABILITY. 125 



Lever at 10° = 1 x sine of angle of 10" -1736 = -17 
20° = 1 X „ 20° -3420 = '34 



>i 



30° = 1 X ,, 30° -5000 = -50 



j> 



40° = 1 X ,, 40° -6427 ^ 64 



) ) 



i) 



0° = 1 X ,, 50° -7660 = -76 



)) 



60" = 1 X „ 60° -8660 = '86 



>> 



70° = 1 X ,, 70° -9396 = -93 



} > 



80" = 1 X ,, 80° -9848 = '98 



> J 



90° = 1 X ,, 90° 1-000 = 1 

To Construct the Curve of Stability (see fig. 84). — Draw 
the horizontal line A B, and upon it at regular intervals mark off 
spaces, each indicating 10** of heel. The 10** spaces may be 
further subdivided into tenths, each representing 1° interval. 
From the point A draw the vertical line A C, and upon this line 
construct a scale of levers of stability, each space representing '1 
of a foot. Using the scale AG set up at the 10°, 20**, 30°, etc., 
intervals, their corresponding leverages, '17, '34, '50, etc., and 
through all these points run a curve. By means of this curve, 
leverage at any intermediate angle of heel can now be readily 
measured. In the figure before us, we see by the diagram that 
the righting lever of stability steadily increases up to 90°, where 




Fio. 85.— Wedges of Immersion and Emersion practically equal 
Sectors of the same Circle for Small Angles of Inclination. 

it attains its maximum length ; after that it gradually decreases, 
exactly opposite to the way in which it increased, until at 180° it 
vanishes altogether. The lever then begins to grow again, no 
longer a righting one, but an upsetting one, and it continues to 
increase up to 270°, where it is longest. After that, it again 
diminishes, until, when a whole revolution has been made at 
360°, the vessel once more becomes stable. 

But the question may be asked — How comes it that for vessels 
of ship form the vertical line through the centre of buoyancy only 
intersects the centre line of the ship at the metacentre for small 
angles of heel up to 12° or 15°, and at larger heels usually does 
not ? The reason is simply this : — 



126 KNOW YOUR OWN SHIP. 

The wedges of immersion and emersion of an actual ship for 
small angles of heel are practically sectors of a circle, and thus 
resemble the wedges with which we have just been dealing, in 
the vessel of cylindrical form, the wedges being exactly equal in 
volume, and practically identical in shape, with their respective 
centres at practically equal distances {x) from the vertical line 
through the centre of buoyancy (tig. 85). So long as these con- 
ditions remain unaltered, the vertical line through the centre 
of buoyancy, at whatever angle the vessel may be inclined, will 
always intersect the line a ft at the metacentre, and when such 
is the case, the distance M G multiplied by sine of angle of heel 
will give the lever of stability, G Z. But in vessels of ordinary 
ship form when inclined to large angles of heel, the wedges of 
immersion and emersion, although exactly equal to each other in 
volume, are dissimilar in shape, with their centres at quite unequal 
distances from the centre of buoyancy. 

Metacentre Curves. — When this is the case, the vertical 
line through the centre of buoyancy does not intersect the line 
a b, fig. 85, at the metacentre.* For large heels the position of 
the point M (originally the metacentre for the upright condition) 
is more difficult to ascertain, and is, therefore, discarded in present 
practice in determining the range of stability. Now, although it 
is advisable for a seaman to thoroughly understand displacement, 
buoyancy, the metacentre, and the principles governing and 
affecting the same, yet it is not necessary for him to enter into 
the mathematical method of calculating the same, for when these 
matters are understood, every necessary information about their 
values may be supplied to him in the form of curves, by the ship- 
builder or naval architect who designs his vessel. Thus we have 
shown in figs. 3, 5, 20, and 21 curves of displacement, curves of 
"tons per inch," and also curves of centres of buoyancy. Since 
these quantities are always the same at particular draughts, all 
that the seaman requires are the curves themselves, the know- 
ledge of their value, and how to read them. The same applies 
to the metacentres. These also are fixed points for ea,ch draught 
for the vessel in the upright position, and, as we have shown, for 
small angles of heel. We shall now proceed to give an illustration 
of such a curve, and show how it is constructed and read. 

The principle of the calculation t for the metacentre of a vessel 
at a particular draught is the same as for a box, except that on 
account of the varying shape of the waterplane, a slight modifica- 
tion has to be made, to find the moment of inertia of the water- 

* The metacentre is a term which ought only to be applied to the point 
M so long as it is constant in position, which is only for small angles of 
inclination. t See Chap. a. for metacentre and other ship calculations. 



STABILITY. 



121 



plane, which, divided by tlie displacement at the particular draught , 
gives tJie height of tJie vietacentre above tJie centre of buoyancii. 
So that, first of all, we require the positions of the centres of 
buoyancy. In fig. 20 a curve of centres of buoyancy is given 
for a certain vessel. This we shall transfer to fig. 86, and set 
oflf the metacentres for the same vessel. 



[ 





%■ 






Scale of heights in ft. above bottom of keel. 

The metacentres, as calculated, were as follows :— 

At 4 feet draught, 10 feet above centre of buoyancy. 
8 ,, 0-2 



H 

o 

< 

H 



EC 
CO 

> 

'A 

< 

H 



Z O 



00 ' 

6C CO 



c 






>} 



)) 



»» 



12 
16 






675 
4 






n 



128 KNOW YOTJR OWN SHIP. 

At the point in the horizontal scale of draughts, representing 
4 feet draught, draw a vertical line intersecting the curve of 
centres of buoyancy, and extending above it. Using the vertical 
scale of feet at the side, set up the height of the metacentre above 
the centre of buoyancy (19 feet), which shows the position of 
the metacentre to be 22 feet above the bottom of the keel. The 
same process is performed at the other waterlines, and when 
all the points representing the metacentres have been set off, a 
curve is run through them, which is that required, and enables 
us to read off heights of metacentres at any draught. 

Unlike the centres of buoyancy and metacentres, the centre 
of gravity is not a fixed point except in certain conditions, and, 
therefore, cannot be supplied to the ship's officer. Every varia- 
tion in the arrangement of weight or cargo, whether it be a 
yacht or cargo steamer, will affect the position of the centre of 
gravity, since, as we have already observed, the centre of gravity 
is the centre of weight. So that about the only conditions in 
which the centre of gravity may be relied upon as occupying a 
constant or fixed position, are, when — (1) the vessel is light, with 
bunkers empty and no stores on board, (2) bunkers full, boilers 
full, and all stores on board, and (3) in the case of cargo vessels — 
the same as 2, with the holds jUled with homogeneous cargoes 
which exactly bring them down to the load draught. To know the 
position of the centre of gravity in conditions 1 and 2 is practically 
all that is required for yachts, whether they be sailing or steam, 
as these are about the only conditions in which they float. But 
for vessels carrying miscellaneous cargoes, perhaps wheat on one 
voyage, cotton on another, coal on another, and so on, the centre 
of gravity may possibly after loading seldom occupy the same 
position twice in succession, so that it becomes advisable to 
ascertain the metacentric height under certain conditions of load- 
ing. We shall, therefore, now endeavour to show how the ship's 
officer may determine the metacentric height himself. 

How to find the Metacentric Height and the Position 
of the Centre of Gravity. — Perhaps some reader is imagining 
that the method will be that described in the chapter on 
" Moments," and it is quite true that the centre of gravity could 
be found by striking a horizontal line at the bottom of the keel, 
and multiplying each individual weight constituting the ship 
and the cargo (shell plating, frames, floors, decks, beams, masts, 
stores, cargo, engines, boilers, winches, windlass, and the host of 
other items) by its height above the horizontal line mentioned, 
and dividing the sum of the moments by the sum of all the 
weights, the result being the height of the centre of gravity above 
the horizontal line. If carefully done, the method would be all 



STABILITY. 129 

Very well, but the immense labour entailed must be evident to 
every reader. Happily, an accurate, as well as a very simple 
method may be adopted, by means of which the centre of gravity 
can be determined in a very short time by experiment. The day 
chosen should be as calm as possible. The vessel, lying either in 
dock or river, should be moored only over stem and stern; no 
ropes abeam, and, if possible, with what breeze there may be 
blowing directly fore and aft, so as to lend no assistance in heeling 
the vessel. Place a known weight with its centre over the centre 
line of the vessel, as near as possible to midships, and capable, 
when afterwards moved to the port or starboard, of inclining 
her 5° or 6°. 

This weight may consist of anything heavy enough in its 
nature, and the centre of which and its weight can be accurately 
determined. Pig iron* may be conveniently used, or blocks of 
ballast iron, etc. These should be carefully ranged over as little 
space, according to the size of the vessel, as possible, and may 
weigh from 1 ton or less, to perhaps 15 or more tons. 

This part of the operation having been carried out, the next 
thing to do is to carefully note the draught at which the vessel 
is floating. Let it be, say, 

13 feet 6 jnches forward J ^ ^^^^ ^^^^^^ ^^ ^^ ^^^^^ 

This, on the displacement scale belonging to the vessel, reads 
1400 tons (see fig. 3). At the centre line of the vessel suspend 
two plumb lines, one forward, and the other aft. Let both lines 
hang freely, and mark clearly a definite length on each of them, 
measuring from the point from which each one hangs, in our case, 
say, 8 feet. Great care should be taken to see that the lines 
hang perfectly plumb on the centre line of the ship» Having care- 
fully arranged all this, we can now proceed with the experiment. 

Let the weight of (say) 12 tons be moved from the centre of 
the vessel, first to starboard, as far as possible, in our example, 
say, 14 feet. This distance of 14 feet is measured from the 
centre of the weight when it was on the centre of the vessel to 
the centre of the weight when afterwards moved to starboard. 
Having done this, on going to the plumb lines it is found that by 
the fore one a deviation of (say) 5| inches has occurred on the 
length of 8 feet, but on going to the aft one the deviation is 
found to be 6 inches. The weights should now be carried to the 
port side, and placed at the same distance as on the starboard 
side, 14 feet from the centre line of the ship. On going again 

* A reliable and most convenieDt method is to fit a large fresh-water 
tank on each side of the ship, and use the weight of water in this (if 
sUffioient} for Inclining purposes. 

I 



130 KNOW YoUR OWN SHIP. 

to the plumb lines it is found that by the fore one 61 inches 
deviation has occurred, and 5f inches by the after. 

If all these be added together and divided by 4, we shall have 
the mean deviation : — 

Port forward = 6J 

„ aft = 5J 

Starboard forward = 6^ 
„ aft = 6 



4)23i 



6 '875 inches. Mean deviation. 

Having obtained this result, the practical part of the experiment 
is now finished, the remainder being a matter of simple calculation. 
Three results have to be found. 

1. The distance the actual centre of gravity has moved to one 
side. Perhaps some reader is saying, " but the centre of gravity 
has not been found." True, nevertheless we can find how far it 
has moved in the direction of the shifted weight. According to 
our study of moments in Chapter II., the rule is : — Multiply the 
toeight moved by the distance it is inoved, and divide the result by 
the total weight. 

Weight moved = 12 tons. 

Distance moved = 14 feet, and the total weight equals the displacemeat, 
which was found to be 1400 tons. 

-— — - — = = 0*12 of a foot = distance the centre of gravity has 

1400 tons displacement 

moved in a line, parallel to the line joining the centres of the weight, 

in its original and in its new position. 

2. The next thing to be done is to find the cotangent of the 
angle to which the vessel has been inclined. This is arrived at by 
difoiding the length of tlie plumb line in incites by the mean deflec- 
tion of the plumb line at that length in inches, 

' = 16*3 = natural cotangent of angle of inclination. 

Although it is not needed in this calculation, still by referring 
to the table of cotangents at the end of the book, it is seen that 
the vessel has inclined to a mean angle of 3^**. 

3. The last part of the operation is to find the metacentric 
height^ or the distance from the centre of gravity to the meta- 
centre. This is done by muHiplying the shift of the centre of 
gravity by the cotangent of tlie angle of heel, 

0*12 X 16*3 ^ 1*95 feet, distance of metacentre above centre of gravity. 

This result is the metacentric height of the vessel in its present 
condition — that is, with the weight used for heeling upon the 



STABILITY. 131 

upper deck. Now it is not likely that this weight will be carried 
in this position when the ship goes to sea. Should the weight be 
placed on board simply for the experiment, with the intention of 
placing it ashore afterwards, a correction must be made in the 
metacentric height, for it is evident that the weight being as we 
now find it, say, 8 feet above the centre of gravity, its eflfect is to 
raise the centre of gravity higher than it would be were the weight 
not there. Therefore, by taking the weight away, the centre of 
gravity must be lower. Then weight removed, multvplied by its 
distance from tJie centre of gravity^ and the result divided by tlie 
total weight, which must be reduced by the removal of the weight, 
will give us the distance the centre of gravity has lowered^ 

12 X 8 96 

= 0*06 of a foot = how much centre of gravity is lowered. 



1400 - 12 1388 

Thus after the removal of the weight, the centre of gravity is 
1-95 + 0*06 = 2-01 feet below the metacentre. 

But suppose the weight used for heeling is one which is 
intended to be kept on board, being perhaps part of the ballast 
iron in the case of a yacht. Then, by lowering the weight into 
the hold again, the eflfect must be to lower the centre of gravity, 
and we proceed as in the previous case. (Weight x distance 
moved -^ displacement = distance centre of gravity has lowered.) 
Measure the distance from the centre of the weight on deck to its 
centre in the new position it will occupy in the hold, say, 15 feet. 
Then, 

12 X 15 

= '12 of a foot = distance centre of gravity is lowered. 

Therefore the corrected metacentric height is 

1-95 + 0*12 = 2-07 feet. 

Having become acquainted with the points known as the centre 
of buoyancy, the metacentre, and the centre of gravity, and to 
some extent the causes affecting them, and having given some 
attention to the wedges of immersion and emersion when the 
vessel is inclined, we are now more capable of pursuing our study 
of the subject, and of endeavouring to understand how the levers 
and range of a vessel's stability are affected under greater angles 
of heel. 

Valuable as a knowledge of the metacentric stability (that is, 
stability at very small angles of heel) of a vessel may be under 
certain circumstances, yet it alone is no safe criterion of a vesseVs 
resource of safety, when exposed to severe weather and subject to 
excessive heeling forces. 



132 



KNOW YOtTB OWN SHIP. 



For example, in the loaded condition one vessel might have a 
metacentric height of, say, 1 foot, which for small angles of heel 
would generally give good righting force, but for greater angles 
of inclination the righting lever might rapidly decrease and soon 
vanish altogether ; while another vessel, with perhaps only 6 
inches metacentric height, and possessing small righting force for 
small angles of heel, might yet have a very long range of stability 
and good righting force at greater angles of inclination. 

It thus becomes evident that further investigation is necessary, 
and we have yet to discover those features in a vessel's design, 
condition, etc., which so powerfully influence her stability under 
all angles of heel. 



No. 



Dimeusions.* 
L. B. D. 
in feet. 



o «•§ 

4) 0) S3 
©^ I— I 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 



100 X 
100 X 
100 
100 
100 
100 
100 
100 X 
100 X 
100 X 
100 
100 
100 
100 X 
100 X 
100 X 
100 X 
100 X 



12 X 10 
15 X 10 
20 X 10 
25 X 10 
30 X 10 
20 X 10 
20 X 10 
20 X 10 

X 
X 
X 

20 X 10 
20 X 10 
20 X 
12 X 

X 
X 
X 



20 
20 
20 



10 

10; 

10: 



;> 
f) 
5 
5 
1 
1 
2 
4 








. 



(5 ' 





•gi^ 


sZ 


O S '- 


■S^^a 


tn**^ .S 


S.d a> 


Centn 
ravity 
attorn 


letace 
Heig 
inFe 


0.5 


fn 


6-3 


-•1 


6-3 


•67 


(5-3 


2 


6-3 


3-9 


6-3 


6-2 


6-3 


2 


6-3 


2 



Kemarks. 



8 



12 
30 
30 



10 
10 
10 
10 
4 



1 
1 
1 
1 
1 
1 
1 



6 
6 
6 
6 
6 

6 I 
6 ' 



16 



6-3 
6-3 
6-3 
8-05 
7-3 
4-3 
2-3 
6-3 
5-3 
6-3 
14-5 



2 
2 
2 

•25 
1 
4 
6 
-•1 

•9 
6-2 
6-2 



Showing effect of increase 
in beam, other dimen- 
sions remaining un- i 
changed. 

Showing effect of increase I 
in freeboard, other di- 
mensions remaining un- 
changed. 

Showing eflfect of variations 
in position of centre of , 
gravity, dimensions re- ; 
maining unchanged. i 



* L = Length ; B = Breadth ; D = Draught. 

To treat of this effectively by means of actual ship stability 
data, would necessitate such a graduated variety of vessels as to 
make such a task a very laborious one. However, this difl&culty 
is easily surmounted. Our purpose will be served by using 
vessels of box shape, which, while simpler in form than actual 
ships, are nevertheless capable of lending themselves to the main 
features we wish to illustrate, and of proving the principles it 
is desired to make prominent. The three great factors upon 
which the stability of any floating objiect depends, whether it be 




nmlt ol rishtliiii 



134 KNOW TOUB OWN SHIP. 

of ship or box form, are beam, freeboard, and position of centre of 
gravity. By means of a series of box vessels, the particulars of 
which are given in the table (p. 132), and the curves of stability 
in fig. 87, the endeavour will be made to reveal the importance 
of each. 

1. Effect of Beam. — Vessels, numbers 1, 2, 3, 4, and 5, with 
the curves of corresponding numbers, will serve for reference 
and examples in this case. Here we have fiwe vessels, each 100 
feet long, 10 feet draught, 5 feet freeboard, and with beams of 
12, 15, 20, 25, and 30 feet respectively. In each case we have 
imagined the centre of gravity to remain stationary at 6*3 feet 
from the bottom of the box, for the depth and draughts being 
assumed to remain the same in each vessel, it is quite reason- 
able to take it for granted that no change would occur in respect 
to the position of the centre of gravity. 

It has already been shown, earlier in this chapter, that 
increase of beam raises the metacentre. This has, therefore, 
happened in the examples with which we are dealing, the result 
being a metacentric height of -0*1, '57, 2, 3*9, and 6*2 feet 
respectively. 

Let us examine the curves of each of these vessels, and see 
what can be gathered from them. 

Curve No. 1 commences with the metacentre 0*1 foot below the 
centre of gravity. In this condition the vessel is incapable of 
floating upright. Will she capsize? The curve answers the 
question most emphatically that she will not. If undisturbed 
she would take a slight list and then lie at rest. If forcibly 
inclined, the righting lever of stability would continue to grow 
in length, until, when on her beam ends (90" on curve), she has 
barely attained her maximum stability. 

There is, however, nothing to elate one very much in the fact 
that a vessel has splendid stability at 90** of inclination, for every 
seaman knows that long before that angle is reached, it would 
be impossible to stand upon or work such a ship, and, moreover, 
weights on board which are considered as permanent and fixed 
would be on the move, and then most disastrous results would 
inevitably ensue. If the levers of stability are good up to 50° 
or 60**, and even then are decreasing and vanish altogether at 
90°, not much fear need be entertained, for rolling to angles of 
even 30"* or 40" on each side is considered very excessive. 

Had we been guided in this particular case entirely by the 
metacentric height, the conclusion might have been come to that 
her condition is much more serious than it actually proves to be. 
Certainly the vessel is too tender ; but what is needed is either 
ballast of some kind in the bottom, if the vesse} is not fjown to 



STABILITY. 135 

the load waterline, or else a re-arrangement of the cargo so as to 
bring the heavy weights lower, and thus increase the metacentric 
height. Either of these methods \vould add immensely to the 
improvement of the vessel's condition. Further observations on 
this type of vessel are made at a later stage, in the remarks on 
"Rolling" and "Behaviour at Sea." 

Curve No, 2. — The diflference between this vessel and the 
previous one is, that owing to an increase of 3 feet in the beam 
the metacentre has been raised, and now the metacentric height 
is 0*57 foot. The curve shows longer levers of stability up to 
90* of heel, where it crosses Curve No. 1. The vessel is there- 
fore stiiFer, and has greater righting force up to this point, but 
her maximum lever of stability is reached sooner than in the 
foregoing vessel. 

Curve No. 3. — The beam is now 20 feet, giving a higher 
metacentre, and a metacentric height of 2 feet. 

Curve No. 4. — Here the beam is 25 feet, with a higher 
metacentre, and a metacentric height of 3*9 feet. 

Curve No. 5. — In this case the beam increasing to 30 feet, the 
metacentre continues to rise, and the metacentric height attains 
6-2 feet. 

Let us see what information can be gathered from these curyes 
for similar vessels increasing in beam only. 

First. With every increase in beam, and consequent increase 
in the metacentric height, the successive curves rise steeper and 
steeper, indicating greater stiffness and resistance to heeling. 

Second. Each successive curve reaches a greater height than 
its predecessor, giving a longer maximum lever of stability, and, 
consequently, a greater righting moment. 

Third. In each successive curve the maximum lever of stability 
is reached at a smaller angle of inclination. 

Fourth. In each successive curve the lever of stability 
vanishes at a smaller angle of inclination. 

Judging from these curves, we might at first be inclined to 
give the entire credit of the great growth in the lengths of the 
righting levers in each successive curve to the increased meta- 
centrip height resulting from the increased beam ; but a further 
comparison of curves will assist us in arriving at a more correct 
conclusion. 

2. Bflfect of Freeboard. — Curve No. 6. — The vessel repre- 
sented by this curve has the same length, breadth, draught, 
metacentric height, and height of centre of gravity above the 
bottom of the keel as No. 3. Instead of 5 feet freeboard she has 
only 1 foot. Mark the effect in the curve. Instead of the 
splendid sweep of No. 3 reaching its maximum lever of 1*9 



136 KNOW YOUR OWN SHIP. 

feet at about 60' of inclination, and vanishing at considerably 
past 90', No. 6 has never more than a lever of 0*2 foot, and that 
at the angle of 20°, the curve vanishing altogether at an angle of 
less than 50°. 

Curve No. 7 is for a similar vessel, with 1 '5 feet freeboard. 
>> " }> >» »> ^ »> >» 

Q 4 

a •'•^ »> )> »> " II )» 

Let us gather again what these latter curves indicate. 

Fi7'st Even good beam with good metacentric height, unless 
combined with suitable freeboard, is no guarantee for either a 
good range or good levers of stability. This is proved by a com- 
parison of Curves Nos. 6 and 7 with Curve No. 3, and comparing 
also No. 17 with No. 5. These two latter are also identical 
vessels, with the exception of the freeboard, which is 1 foot 6 
inches in the former and 5 feet in the latter. The great diiFer- 
ence in the curves, which can only be attributed to the diiFerence 
in the freeboard, is very apparent. 

Second, Increase in freeboard with undiminished metacentric 
height, increases not only the length of the levers, but the 
maximum lever in each case is at a greater angle of inclination, 
and the range of stability is lengthened out also. Curves Nos. 
6, 7, 8, 9, and 10, with their increasing freeboard, prove this, 
each of the first four in its turn approaching No. 3, until No. 
10, with the great freeboard of 8 feet, far surpasses it in both 
maximum levers of stability and range. 

It may be all very well to make the statement that freeboard 
has this and the other effect upon a vessel's stability ; but some 
reader may be asking the question, " How is it that freeboard is 
capable of producing such an effect 1 " An endeavour to explain 
this will be made by the aid of the following graphic illustration 
(fig. 88). 

Figs. i. and ii. are the vessels in the table, Nos. 8 and 3 
respectively. They are similar to each other, except that i. has 
2 feet, and ii. 5 feet freeboard. Floating in the upright condi- 
tion, they have exactly the same metacentric height, 2 feet. 
Let fig. i. be heeled until the deck edge is down to the level 
of the water, as shown in fig. iii., the angle of inclination 
being 10°. To find the lever of stability we must turn our 
attention to the centre of buoyancy. Let fig. x. represent 
the buoyancy of the vessel, which corresponds in every respect 
to the immersed part of fig. iii. The centre point in fig. x. is 
B, and this is the centre of buoyancy. By transferring the 
position of B to fig. iii., we see its position in relation to the 
centre of gravity. The distance between the vertical linea 



137 








• • 




vm 








VII 






1 














1. 




":&.- z. T 








— -" 




c 


. — 


— _ . 






a 


.0. _ 










a 


1 
1 

1 








■ 











Fia. 88,— fS^OWINO EJffllOT Of f'REBftOAUp ON STAfiJI^ITT, 



138 KNOW YOUR OWN SHIP. 

through these points is the lever of stability, and since it inter- 
sects the centre line, P, above the centre of gravity, it is a 
righting lever. Although the shape of the buoyancy has altered 
in form under the inclination, owing to the transference of the 
wedge of buoyancy shown by the hatched lines, to the other 
side of the vessel, indicated by a black wedge, yet its volume is 
unchanged. The centre of buoyancy, therefore, travels in the 
direction in which the buoyancy is transferred, just in the same 
manner as shifting a weight upon a lever, the distance in the 
case of the wedges being reckoned from centre to centre. 

Turning to fig. ii. with the greater freeboard, on inclining this 
vessel to the same angle 10**, her deck edge is still considerably 
out of the water (fig. iv.). However, in this condition her form 
of buoyancy is similar to fig. iii., simply because the wedges of 
immersion and emersion are identical in shape. The centre of 
buoyancy, therefore, occupies the same position, and it follows 
that the lever of stability must be similar to that in fig. iii. 

Let fig. ii. be now heeled until its deck edge reaches the 
waterline, as shown in fig. vi. The reasoning applied to ^g. iii. 
will apply in this case also : — A wedge of buoyancy has been 
transferred from one side to the other, giving the form of 
buoyancy shown below the waterline, the centre of which is 
the centre of buoyancy, B. This point again shows the relation 
of the centre of buoyancy to the centre of gravity, and the 
lever of stability is found to have increased simply because a 
larger wedge has been transferred a distance of ^• to g (the centres 
of the wedges from each other). 

Fig. i. at this angle of inclination shows a different state of 
affairs (see fig. v.). There is certainly a wedge of emersion, but 
owing to the decreased freeboard, there cannot be a similar 
wedge of immersion. The dotted line indicates the boundary of 
the greater buoyancy of fig. vi. Now, supposing fig. v., when 
inclined, to float at the waterline W L with the wedge of 
emersion K, then there ought to be a wedge similar in volume 
immersed. But this cannot be, for the immersed wedge is 
deficient by the volume of the small wedge indicated by the 
hatched lines in the diagram. Now, the volume of the emerged 
part, of whatever shape, must equal the volume of the immersed 
part, and since the immersed wedge is deficient by the small 
wedge already referred to, this loss of buoyancy can only be 
regained by the vessel sinking to a deeper draught, thereby 
spreading thei buoyancy of the lost wedge along the waterline, 
and thus causing the vessel to float at the new waterline wL 
The black part in the figure shows the new immersed buoyancy. 
The important '>T)oint is to fipd wha,t effect this new immersed 



> 



\ 



STABILITY. 139 

buoyancy will have upon the lever of stability. The more 
buoyancy that can be placed towards the side to which the 
centre of buoyancy has already begun to move, the further will 
this point be brought towards that side. Owing to the lower 
freeboard the loss of the hatched wedge of buoyancy has robbed 
the vessel of a most effective agent in bringing out the centre of 
buoyancy from the centre of gravity, and by placing this lost 
buoyancy along the waterline, a further check is made upon the 
outward movement of the centre of buoyancy, and the tendency 
is to draw it back again ; hence the decreased lever of stability, 
as compared with fig. vi. Passing now to the conditions shown 
in figs. vii. and viii., we find these vessels heeled to an angle of 
90". The centre of buoyancy can easily be determined in these 
cases. For fig. vii. it will be half the distance from the bottom 
(not the bottom of the figure, but the bottom of the ship) to the 

deck, which is — - — = 6 feet, and the centre of gravity being 

6*3 feet, the result is an upsetting or capsizing lever of 0*3 of a foot. 
Fig. viii., however, has the advantage of the buoyancy afforded 
by the additional freeboard shown beyond the dotted line. 
This naturally tends to draw out the centre of buoyancy, and its 

position now is — = 7'5. 7*5-6*3 = 1*2 righting lever. 

The foregoing remarks, with a little study of the figures them- 
selves, will leave little doubt in the mind of the reader of the 
importance of freeboard as a factor in affecting stability. 

3. Effect of Position of Centre of Gravity. — Let us take 
our final illustration, and note the eflfect of obtaining metacentric 
height, not by means of increasing the beam, and thereby raising 
the metacentre, but by retaining the same beam and same posi- 
tion of metacentre, and lowering the centre of gravity. 

This may be done to a considerable extent in merchant 
steamers, in loading miscellaneous cargoes, by keeping the 
heavy weights low, but to a very much greater extent can it 
be done in yachts, where the centre of gravity can almost be 
placed wherever desired by means of permanent ballast. 

Cui-ves No8. 11, 12, 7, 13, and 14 are for vessels 100 feet long, 
20 feet broad, and 10 feet draught, with 1 foot 6 inches freeboard, 
the metacentre being, therefore, at the same height from the 
bottom of each vessel — viz., 8' 3 feet. The only difference between 
them is in the height of the centre of gravity. 

For No. 11, the centre of gravity is taken at '25 foot below the metacentre. 

>» ^^i it >i 1 I' >» 

,, •» >» I) ^ leet ,, 

>» ^^t >i it ^ >» >> 



140 KNOW TOUR OWN SHIP. 

The effect of this alteration in the position of the centre of 
gravity is shown by the curves. Firsts at a particular draughty 
by every downward movement of the centre of gravity, thereby 
causing an increase in the metacentric height, both the levers and 
range of stability are lengthened. Second, each curve rises more 
steeply than its predecessor, indicating greater stiffness. 

We have already seen the effect of beam upon stability. 
Suppose 10 feet be added to the beam of a vessel identical in 
every respect with No. 14. The effect is to raise the metacentre, 
and give much greater metacentric height. But let the centre of 
gravity also be raised from 2*3 feet from the bottom of the vessel 
to 6*3 feet, the metacentric height being now 6-2 feet, the result 
is to give a vessel identical with No. 17. Nos. 14 and 17 differ 
now practically in beam only. 

An error is sometimes made in a case like this, it being 
imagined that the broad vessel, even with the same metacentric 
li eight, is better than the narrow one of the same depth and 
freeboard. If the curves of these two vessels be compared, their 
stability is seen to be widely different, the narrow vessel possess- 
ing more stability in every respect than the beamy one, except 
perhaps at the beginning of the curve. 

Now how does this happen ? In the first place, the advantage 
of the increased metacentric height, which was obtained by the 
increased beam, was robbed from the vessel by raising the centre 
of gravity, and making the metacentric height similar in both 
cases. Perhaps some reader is still saying — " Having made the 
metacentric height similar for both vessels, why are the curves 
not similar?" This is just where the error is often made in 
depending upon the metacentric stability, which, as has been 
previously stated, is no guide for a vessel's range of stability, 
but only for small angles of inclination. Up to 7° or 8° these 
curves are approximately the same. For gi*eater angles of in- 
clination, we must turn our attention to the centre of buoyancy, 
and trace its movements in relatioa to the position of the centre 
of gravity. 

In A and B, fig. 89, no levers of stability are seen, since the 
vessels float upright and are perfectly stable, with the centre of 
gravity, centre of buoyancy, and metacentre (the last not indi- 
cated) in the same vertical line, a h. In figs. C and D the same 
vessels are inclined to angles of 45**. It is now seen that the 
levers of stability in this condition are very different, those for 
tlie smaller vessel being much the greater. Both the centre of 
buoyancy and the centre of gravity, though chiefly the latter, 
are accountable for this result. Turning our attention first to 
tUe centre of buovancv, we ftnd that, in both figs. C apd D, 



STABILITY. 



141 



CL 




CU 



B 






^ 





.'S 



b^ 



C 



B 



—a^ 



F,-~ 



K 



B 






! I 



Of 



Fig. 89. — Comparison of Vessels with different Beams but similar 

Metacentric Heights. 



142 KNOW YOUR OWN SHIP. 

owing to the small freeboard in each case, the deck edge has 
become immersed when inclined to a very small angle. This at 
once checks the outward movement of the centre of buoyancy 
though fig. C, owing to its smaller beam, has the advantage to 
some extent, since greater inclination would be needed to immerse 
its deck edge than would be required for fig. D. 

Turning now to the centre of gravity in each case, we find here 
the chief factor in producing the great dijfference in the stability 
levers. It is first noticed that their difference in position from 
the bottom of each vessel on the line a & is very great, although 
the metacentric heights in the upright condition are practically 
identical. In fig, B it was easy to get a good metacentric height, 
owing to the great beam, but in fig. A the greatly reduced beam 
made it necessary to very much lower the centre of gravity, in 
order to get the same metacentric height. Hence the difference 
in their positions. It will also be observed that the lower fJie 
position of tlie centre of gravity is on the line a b, the greater 
viicst be the righting lever of stability (a glance at the figures 
will show this clearly), and on the other hand, the higher the 
position of the centre of gravity on the same line, the smaller 
the lever. This, then, accounts to a great extent for the difference 
in the levers of stability. So that even on their beam ends, at 
angles of 90**, we still find the narrower vessel (fig. E) with a 
large righting lever, while the broader one, F, has actually an 
upsetting lever. 

However, the case we have taken is certainly an extreme one 
for cargo or passenger vessels, for while in the broad vessel the 
position of the centre of gravity would very often be found high 
in comparison with the depth, in the narrow vessel, it would be 
impossible to load her and have the centre of gravity as low in 
comparison with the depth. Were the two vessels loaded in the 
same manner — that is, in relation to the vertical position of the 
weights of the cargo, the centre of gravity in both vessels 
occupying the same position from the bottom of the box 
— a vastly different result would arise. Let the centre of gravity 
of the narrow vessel be raised by the loading of cargo to the 
same position as in the broader one — viz., 6*3 feet from the 
bottom of the vessel. The dotted lines on the figures show the 
new vertical line through the centre of gravity of the nari'ow 
vessel, and curve No. 7 will show the whole range of stability. 
The tables are now turned against the narrow one, indicating 
much reduced stability. Hence the necessity of wisdom in load- 
ing, as, in the latter ifease, the heavy weight of the cargo would 
have to be placed muclr*. lower in order to get anything approach- 
ing similar levers of stabSity for the two vessels. 

\ 



STABILITY. 



143 



But while the position of the centre of gravity at 2*3 feet from 
the bottom of the vessel for curve No. 1 4 is an exaggerated case 
for merchant vessels, it is by no means out of the way for sailing 
yachts, for m order to get great stiffness and long levers of 
stability, which are necessary to carry great sail area, especially 
with small beam, the method of bringing the centre of gravity 
very low by placing ballast either in the keel, or else as low as 
possible, has to be adopted. 

Before leaving this part of the subject of stability, the reader 
IS again warned against jumping to the conclusion that even a 



.5^ 



SB 
go 




•— V - 



1 

so' 



'AO' 



70' 



— T— 

SO 



— 1 

.9/7' 



CC 



Scale of angles of inclination in degrees. 




Inclination showing maximum lever of stability. 

Curve of stability for a sailing ship, 270 feet long, 41 feet beam, and 26 feet 3 inches 
depth, in a light condition, with about 112 tons of ballast on board. Metacentric height, 
2-tt feet. Centre of gravity, 20^ feet above the top of the keel. Freeboard, 17i feet. 

FlO. 90. 



combination of good beam, good freeboard, and good metacentric 
height will always produce satisfactory stability. This has 
already been shown by the several box vessels and their curves, 
and will further be emphasised by a glance at the curve of 
stability (fig. 90), which is for a sailing ship in a light condition. 
She has 41 feet beam, 2*9 feet metacentric height, and 17^ 
feet freeboard, the last of which is extremely great, and yet 
the curve of stability in this condition represents both short 
levers and very short range, this being attributable to the fact 
that, in the light condition, the heavy top weight of masts, 
spars, etc., brings the centre of gravity very high, and it haa 



144 KKOW tOtJJft OWN SHlt». 

already been pointed ont that the higher the centre of gravity, 
the shorter are the levers of stability, and the sooner does the 
vertical line through the centre of buoyancy intersect the centre 
line of the ship below the centre of gravity, thereby creating a 
capsizing moment. The same vessel in her loaded condition, 
with only 5J feet freeboard and 3 feet metacentric height, would 
have both immensely greater levers, and greater range of stability, 
because then the centre of gravity is much lower in its position. 

In a box vessel, say, 20 feet deep, if the centre of gravity be 
at half the depth, the righting Jever of stability must vanish at 
90** of inclination, whatever be the freeboard, since in this con- 
dition the centre of buoyancy and the centre of gravity are in 
the same vertical line. If the centre of gravity be higher than 
half the depth, the levers will be shorter and the range less also, 
but if the centre of gravity be lower than half the depth, then 
the levers will be longer, and the range will extend beyond 90** 
of inclination. Now, all actual ships are not of box form, though 
it is granted that in some cases it is somewhat difficult to draw 
that distinction. Of two vessels of similar beam and depth, the 
one with most buoyancy in the upper half of her depth, being 
therefore most fined away at the bilge and bottom, can afford 
to have the centre of gravity the higher, and the nearer the box 
section is approached, the lower must be the centre of gravity. 

The actual box ship is, therefore, the worst case, since it 
brings the centre of buoyancy into the lowest possible position ; 
and, on the other hand, the vessel fullest at the waterline, and 
well fined away below, has its centre of buoyancy in the highest 
possible position, in which position the longest levers and the 
greatest range of stability are produced, other features in the 
design being favourable. It is thus impossible to stipulate a 
particular position for the centre of gravity applicable to all 
ships. 

For a box-shaped vessel, if the centre of gravity is from about 
0*5 to 0*6 of the depth from the top of the keel, with fair meta- 
centric height, a fairly good range of stability may be expected, 
though the righting levers may be small under certain circum- 
stances. For vessels of finer underwater form greater stability 
would be developed, and when the centre of gravity is less than 
0'5 of the depth from the top of the keel, great stability may be 
anticipated. 

Effect of Tumble Home, — In fig. 91, let G be the centre 
of gravity, B the centre of buoyancy in the upright posi- 
tion, CDE the immersed wedge, and K the centre of the 
immersed wedge. 

The greater the distance from the original centre of buoyancy, 



STABILITY. 145 

B, to the centre of buoyancy of the immersed wedge, K, as 
shown by the line P, the greater will be the eiFect in drawing 
the centre of buoyancy out from its original position. Let B' 
be the new centre of buoyancy when inclined, and GZ the 
righting lever of stability. 

Now, supposing a piece of the shape of the black wedge be 
cut oflf from the vessel, let us observe the eflfect upon the 
stability. Owing to the loss of this buoyancy when inclined, 
compensation must be made by apparently drawing upon the 
reserve buoyancy, and taking a layer off all along the waterline 
to the dotted line, simply because the wedge of immersion is 
now less than the wedge of emersion ; and they are equalised by 
adding a layer to the wedge of immersion at C D, and deducting 
a layer from the wedge of emersion at W C. 

The centre of the immersed wedge, K, will have travelled 




Fio. 91.— Effect of Tumble Home on Stability. 

towards the left of the figure, causing B' to move in the same 
direction, and the layer of buoyancy along the waterline, W to C, 
will also have aided to produce this effect. 

6Z will now have become shortened, which means reduced 
righting moment of stability. 

Taking the case of a vessel *of ship form, we can easily see the 
applicatioi\ of the above illustration. Instead of carrying the 
sides up perpendicularly they are usually curved in, as shown 
in fig. 15. This is known as tumble home. A valuable piece 
of buoyancy is lost ; in fact, the very part of the wedge which 
is most efficacious in drawing out the centre of buoyancy from 
the centre of gravity is cut away. Thus in vessels of low free- 
board, and especially if at the same time possessing narrow beam, 
the effect of much tumble home may be to assist in causing 
deficient stability in certain conditions. However, as it is not 
usual to give an ordinary mercantile vessel more than a few 



U6 



KNOW YOUR OWN SHIP, 



inches of tumble home at the main deck, the effect is not serious 
in the ordinary types of modern broad beamed cargo steamers. 



& 

g 
«> 






•a 

o 
03 




Scale of Angles of Inclination in Degrees. 

Curves of stability for a cargo steamer— Length, 480 ft. ; beara, 67 ft. ; depth, 40 ft. 
Curve No. 1, Light condition, metacentric height, 2 68 ft. 
2, Load „ „ 3-67,, 



»> 




Scale in Degrees. 

Curve for a steamer 410 ft. long, 50 ft. 6 ins. beam, 32 ft. depth. 
No. 1, Light condition, metacentric height (G M) = 11-06 ft. 
No. 2, Loaded with homogeneous cargo, 7 ft. 6 ins. freeboard, G M 1*85 ft. 
No. 3, Same as No. 2, with coal consumed. G M 1-68 ft. 
Note.—l ft. in the scale of levers in this figure is equal to 2 ft. for No. 1 Curve. The 
levers are thus only half length on this diagram. 




00' 



W 



80' 



ito 



30 ^o' SO' 

Scale in Degrees. 
Curve for a vessel 360 ft. long, 45 ft. beam, 30 ft. 1 in. depth. Metacentric height, 1*48 ft. 

Figs. 92, 93, and 94 are Examples of actual Ship Curves. 

A point which is sometimes overlooked on the part of the 
owner or his representative in the design of a new vessel, is the 
value of sheer. TUut it adds to the uppearauce, gives valuable 



STABILITY. 147 

rising power, and tends to prevent the shipping of water over 
the stem and stem, must be clear to everyone. 

But one of its best features is that it produces increased free- 
board, the use of which has already been discussed. 

Stability in difterent Types of Vessels. — As regards types 
of vessels best adapted to produce good stability when of suit- 
able dimensions, and the loading properly carried out, those 
with most freeboard must come first. 

Thus we have the awning-deckery with its completely closed-in 
light superstructure between the main and awning decks, 
splendidly adapted for carrying passengers or light cargoes. 

Next comes the spar-decker with a stronger superstructure, 
and adapted for carrying cargoes of greater density with smaller 
freeboard in comparison with the awning-decker. 

Last, we have the strongest type of ship, the two or three 
decker. This is the best deadweight carrier, having least freeboard. 
Unfortunately, structural strength and stability are in no way 
related to each other, and thus, as statistics prove, especially the 
older types of these vessels, with their small beam to depth, and 
also small freeboard, have produced the most disastrous results, 
through lack of stability. A vessel which has found great favour 
among shipowners during late years, because of its special adap- 
tation for certain trades, is the raised quarter-decker^ which is 
simply a modification of the strong two or three deck type pre- 
viously referred to, and whose comparatively greater freeboard 
assists in producing more favourable stability. (See also page 192 
for further remarks upon types of vessels, etc.) 

Note, — Awning- and spar-decked ships are equally as strong as three- 
deckers in relation to the deadweight they carry at their respective load lines. 



H8 KJ^OW TOUR OWJT SHIP 



CHAPTEK VI. (Section II.) 

ROLLING. 

Contents. — Rolling in Still Water — Relation of Stiffness and Tenderness 
to Rapidity of Movements in Rolling — Resistances to Rolling — Danger 
of great Stiffness — Rolling among Waves — Lines of Action of Buoyancy 
and Gravity — A Raft, a Cylinder, and a Ship among Waves— Syn- 
chronism, how Produced and Destroyed — Effect of Loading upon 
Behaviour — Effect of Transverse Arrangement of Weights upon Rolling 
Motions — Alteration in Behaviour during a Voyage — The Metacentric 
Height — Fore and Aft Motions — Fore and Aft Arrangement of Weights, 

Boiling. — After the consideration already given to the subject 
of stability, we are now able to proceed further, and observe the 
relation between stability and rolling at sea, and what means 
can be adopted to reduce the latter to a minimum. 

Rolling is often spoken of as though it were a particular 
quality belonging to a ship. For instance, it is not uncommon 
to hear a ship described as a heavy roller ; or another, as being 
very steady. A little investigation will show that it is not 
strictly correct to so characterise any vessel. At the same time, 
however, we shall see that the design of some vessels lends more 
encouragement to rolling than others; and, on the other hand, 
it is possible to a considerable extent to overrule even the 
influence of design, and make a vessel either steady, or specially 
inclined to heavy rolling, in spite of design. 

Let us briefly enumerate the points we have already studied, 
which will help us. 

First, — If a vessel rolls under the influence of some external 
force, the power she possesses which brings her back to the up- 
right is her stability. 

Second. — If a vessel has a great metacentric height, it follows 
that, at least for small angles of inclination, she possesses con- 
siderable righting moment, and the curve representing levers of 
stability will rise the more steeply the greater the metacentric 
height. Such a vessel is said to be stiff. 

Third, — If the metacentric height is small, the reverse of the 
previous case will be the consequence, the righting levers will 



"be stiiall for small angles of inclination, and the curve of 
stability will rise slowly. 

The effect of metacentric height in relation to rolling is exactly 
the opposite to what one would at first imagine. The stiff ship 
with great metacentric height offering great resistance to inclina- 
tion, is the very one which generally rolls most in a seaway ; 
and the tender vessel, with small metacentric height and small 
resistance to heeling, is usually the steady one. How comes 
this ? We shall be better prepared to answer if we make a few 
mental experiments upon a vessel for ourselves. 

Rolling in Still "Water. — Let us imagine a ship with large 
metacentric height and a fair range of st^ability to be lying in 
the dock. By means of some external force let the vessel be 
heeled over to, say, 10" of inclination, and held there. We 
know that the centre of buoyancy will have shifted into the 
centre of the new shape of displacement, and there is now 
created a lever between the vertical lines passing through the 
centre of gravity and the centre of buoyancy. It is, therefore, 
evident that the vessel possesses an amount of righting force 
exactly equal to the external heeling force required to so heel 
her, and by means of which, when the latter is removed, she 
will come to the upright. In this position the available right- 
ing moment will have disappeared, since the centre of gravity 
and the centre of buoyancy are again in the same vertical line. 
Moreover, the greater the metacentric height the greater the 
amount of available righting moment, and thus the more rapidly 
will she reach the upright position. 

Resistances to Rolling. — Let us now free our vessel lying at 
the angle of 10°. The result is, that in the space of a few seconds 
she has reached the upright. But does she remain there ? Not 
at all, for just as in the case of a pendulum in travelling from 
an angle of inclination to the vertical, an amount of energy of 
motion {kinetic energy) is accumulated, which carries her over to 
the other side, where again a righting lever is created acting in 
opposition to the last roll. Were there no resistance of any 
kind this process of rolling would be endless; but experience 
shows us that after a series of rolls, the vessel will come to rest. 
This is brought about by the united action of several kinds of 
resistance. 

First — T\\Q friction of the air upon the exposed surface of the 
vessel. 

Second. — The friction of the water upon the immersed surface. 

Third, — Head resistance, caused by projections on the immersed 
surface. 

Fourth, — Wave resistance. 



15() 



KNOW ¥otJfe oWiJ sMii^. 



As the great object is to get a safe and steady ship, let us Bfee 
how far it lies in our power to modify these resistances. 

Nothing can be done to increase the air friction, unless it be 
by means of sail, which will certainly tend to produce steadiness. 
It would be an easy matter to make a rough skin upon a vessel ; 
but this would deduct so enormously from the speed, that it is 
preferred to get the smoothest surface possible. In the third 
case, however, a very great deal may be done to produce steadi- 
ness by fitting projections in the form of keels or bilge keels. 
The day of doubt as to the efficiency of this means is past. Not 
only are naval experts agreed, but the testimony of every seaman 
who has experienced the efficacy of bilge keels, especially when 
fitted upon vessels which had previously been without them, is 
unanimous as to their great value in reducing both the number 
and angles of roll, or osciUations. 

By an oscillation is meant a complete roll from port to star- 
board, and the time occupied to perform such oscillation is 
termed the period of oscillation. An example, taken from the 
experiments of the late Mr. Froude, upon the model of the war 
vessel "Devastation," will serve as an illustration in passing : — 



Number and Descriptiou of 
Bilge Keels. 



1. No bilge keels, . ' . 

2. One 21 inch bilge keel on each side, 
! 3. ,, 36 

4. Two 36 

5. One 72 



i> 



II 



>> 



II 
}i 
II 



Number of double 
Oscillations before 

Vessel was 
brought to rest. 



3U 

12i 

8 

4 



Period of double 

Oscillation in 

seconds. 



177 

1-9 

1-9 

1-92 

1-99 



In speaking of wave resistance, we do not refer to sea waves — 
for, as was formerly stated, the vessel upon which we are experi- 
menting is supposed to be lying in a dock — but to waves created 
by the vessel in her rolling movements in the water. Such 
might at first appear to be very trivial, but to create such waves, 
even though very small, means an immense expenditure of 
energy, and this, therefore, must be deducted from the total 
available energy, which incites the vessel to roll. The combined 
efiect of these agencies is to diminish the angle of inclination, 
and, finally, to produce extinction. A noteworthy point to be 
observed, as shown by the above table, is that for moderate 
angles of inclination the period is approximately the same for 
the larger as for the smaller oscillations. Thus we see that it 



ROLLING. 151 

is great stability which conduces to rapidity of rolling motion, 
though not necessarily to great angles of inclination. 

Danger of great Stifl&iess. — The danger of very stiiff vessels 
with good range of stability is, not that they will capsize, but by 
the severity of their movements that they will damage them- 
selves by straining the structure and causing leakage, or by 
shaking their masts overboard, not at all an unheard-of-occur- 
rence, where broad-beamed sailing-ships, owing to pure ignorance, 
have been ballasted in a manner producing enormous stiflfness. 

On the other hand, the vessel with the small metacentric 
height, when forcibly inclined to the same angle of 10°, and then 
set free, returns to the upright much more slowly, having shorter 
righting levers, and, therefore, less stored energy. The energy 
of motion acquired in returning to the upright is less, and adding 
to this the resisting agents, it follows that the angles to which 
she rolls, and the number of oscillations before coming to rest, 
will be reduced. 

The nearer the immersed portion of any object approaches the 
shape of a circle, and the nearer the metacentre and the centre 
of gravity are together, the less power to regain the upright will 
it possess until we reach the minimum in the actual cylindrical 
type with the centre of gravity and the metacentre coincident. 
Vessels of this latter type possess no righting force at all, and 
thus, when inclined to an angle, they remain there, even though 
entirely free. A very small external force, therefore, will heel 
them, and turn the underside uppermost altogether. 

Rolling among Waves. — Now the question arises, since the 
motion of rolling is so governable, is it better to have the steady 
type of ship with small metacentric height, or the stiff one with 
great metacentric height ? But this we shall better answer if we 
first briefly consider her more complicated motions among waves, 
as thus far our considerations have dealt exclusively with vessels 
in still water. Here, however, peculiarities arise, and although 
the principles deduced from forced rolling in still water still 
hold good to a great extent, we shall find our ship behaving very 
differently at times from what we should imagine if we depended 
solely upon our knowledge of rolling in still water. In the first 
place, it is scarcely necessary to inform any reader who has ever 
noticed a piece of wood floating in the sea among unbroken waves, 
that it is not the mass of water composing the waves which 
moves onward, but the form only. A slight forward and back- 
ward motion of the floating object shows that the only move- 
ment of the wave water is slightly forwards and backwards. 
At a comparatively small distance below the surface of the water 
there is apparently no motion whatever. An old, though not 



152 



KNOW YOtJft OWN SHIP. 



strictly correct, illustration is that of wind blowing over a field 
of corn, causing a waving motion as the heads incline with the 
gusts of wind, and then rise again. 

Raft, — As a complex form like a ship is a form more difl&cult 
to deal with than that of a flat floating piece of wood, let us 
examine, first, the behaviour of a small raft. In smooth water 
we know that, owing to its great stiffness, its oscillations are 
exceedingly rapid and its period very short, and that a condition 
of rest is soon obtained. 

We have also noticed that, when among wave water (figs. 95 and 
100), its deck is always parallel, and the mast perpendicular to the 
surface of that part of the wave upon which it is floating. It is 




LENgr H . or Wave. ^ 



Fig. 95. — Behaviour of a Small Raft among Waves. 

therefore upright on the summit and in the trough of each wave, 
and its greatest angle of inclination is at about half the height 
of the wave where the slope is greatest. In this case the raft, 
being very small, behaves practically as though it were actually 
a particle of the surface wave water. Such agreement becomes 
less and less as the beam increases relatively to the length of 
wave, as it can no longer lie flat on the surface, or have the 
greatest angle of inclination where the wave slope is greatest, 
until at last, where exceptionally large beams are reached, as in 
the Czar of Russia's yacht "Livadia" (153 feet), the vessel no 




Fig. 96. — Illustrating a very Beamy Vessel among Wavf^. 

longer takes of the motion of a small raft at all, but maintains 
a comparatively horizontal deck, as in fig. 96. 

The longer the waves are in comparison with the breadth of 
such a vessel, the greater inclination she would reach in 
endeavouring to follow the angle of the wave surface. But in 
a short sea she would be practically steady. 

Cylinder, — Let us take as another example a vessel of the 
cylindrical type. 



ftottlKO. 



153 



In fig. 9? we see the object as it would float in smooth 
water. Being of wood, and of equal density throughout, the 
centre of gravity is in the centre, as is also the metacentre. 

The centre of buoyancy is in the same vertical line through 
this point, and the object floats at rest, as it will do at any 
angle of heel, since it never has any stability ; a state which can 
only exist when there is no righting lever, the vertical lines 
through the centre of gravity and the centre of buoyancy always 
coinciding. 

In fig. 98 we see the same object among waves, and on a 
wave-slope. Let us examine its condition now. 

From observation every reader knows that no revolving or 
heeling motion occurs. The line ah remains vertical, and the 



—B 





Fig. 97. — Behaviour of a 
Cylindrical Vessel in 
Smooth Water. 



Fig. 98. — Behaviour of a Cylindrical 
Vessel among Waves. 



waterline varies from R S, when floating in still water, or on the 
crest, or in the trough of the wave, to XY, the greatest wave- 
slope. But on examining the object on the wave-slope, it is 
found that the centre of buoyancy has shifted into the centre of 
the imm^ns^d part. If we drop a vertical line through the centre 
of gravity and through the centre of buoyancy, we see that these 
points are no longer in the same vertical line, but that a distance 
exists between them. If this distance represents the length of 
the lever of stability, the vessel cannot remain in this condition 
without making some effort to bring the centre of buoyancy and 
the centre of gravity into the same vertical line, which effort 
must incline the vessel more or less. But observation proves 
that such is not the case, for the object makes no movement to 
the one side or the other, the only interpretation of such 
behaviour being that no lever whatever exists, and that the 
downward force of the weight of the ship and the upward force 



154 ki^oW IrouR OWN stiii^ 

of buoyancy are evidently being subject to other forces causing 
them to act differently from the manner in which we have been 
accustomed to consider them in still w^ater. It is just on this 
point where many of those, whose knowledge of the subject of 
stability, etc., is very limited, are apt to come to a wrong con- 
clusion regarding the behaviour of ships among waves. 

It is this apparently contradictory behaviour of ships which 
has given rise to so many theories on the subject. But it was 
not until the late Mr. Froude brought forward the now generally 
accepted wave theory that so much light has been thrown upon 
the subject. To discuss at length the theory of deep sea waves 
would form a volume in itself, and therefore lies outside the aim 
of a book such as this. Those wishing to pursue this branch of 
the subject can find ample information in the volumes of the 
Institute of Naval Architects, and also in the admirable works 
mentioned in the preface. We can, however, make a few brief 
observations, borrowing from the theory mentioned, such 
principles as may be of assistance to men of practical experience 
at sea, the class of men which it is the chief aim of this work to 
assist. 

A feather in the air would fall in a straight line to the earth 
if there were no wind, owing to gravitation. Such fall, however, 
is always more or less overruled by the force of the wind when 
wind is blowing. Again, an iron plumb ball suspended from a 
cord, would hang vertically, if undisturbed, owing to the down- 
ward attraction of gravitatioa On approaching it with a magnet 
sufficiently close to produce induced magnetism, gravitation is 
interfered with, and the iron ball seeks to follow the magnet. 
These instances are related simply to show that under certain 
circumstances the power of gravitation (such as causes the weight 
of a ship to act through its centre of gravity in a vertical line) 
can be over-governed by the introduction of other forces. Thus 
in waves we have what is termed centrifugal force^ which, acting 
along with the gravitation force, gives a resultant force approxi- 
mately perpendicular to the wave surface."* Turning to fig. 98, 

* If centrifugal force were approximately perpendicular to the wave surface, 
the fluid pressures in waves could not possibly be perpendicular to the wave 
surface also, for gravity would show itself by producing a resultant which 
would certainly not be perpendicular to the existing wave surface, but con- 
siderably deflected from it ; but this is impossible, since the wave surface at 
any point, at any moment, is perpendicular to the instantaneous resultant of 
several forces, of which the centrifugal force is one. 

Referring again to fig. 98, though the cylinder is on a wave slope, gravity 
still acts vertically through its centre of gravity G, and were gravity the only 
force exercising any influence upon the cylinder, it would cause the cylinder 
to slide down the wave slope, biit this does not happen, for here again we find 
that the natural vertical force of the weight of the cylinder is interfered with 



i^oLLitTG. 



155 



We can now better understand how it happens that no righting 
lever was set up, the reason simply being that the lines of action 




Deck almost parallel to wave-slope, 
with lines of action through G and B 
practicaUy coincident. This is the 
virtual upright. 

Fig. 99.— Behaviour of a Ship among Waves. 

through the centres of buoyancy and gravity coincided, as shown 
by the arrowed line. 

by the internal wave forces, producing a resultant which is the virtual upright, 
approximately perpendicular to the wave surface, and therefore parallel to the 
resultant buoyancy pressures in the wave. Thus an instantaneous position of 
equilibrium is set up without any tendency whatever for the cylinder to slide 
down the wave slope. 

Where the water surface is horizontal, the buoyancy pressures act in 
upward vertical lines. This is as true for the smooth surface of the vast 
ocean as for the water in a bucket. And even when waves have been 
created, the upward pressures from the ocean depths are in nowise changed. 
But on coming to the actual waves themselves (which are only surface dis- 
turbances extending to a very small depth as compared with the depth of the 
ocean), we find that the buoyancy pressures are now exerted in lines of action 
approximately perpendicular to the wave surface. 

It is not supposed that this theory, known as the *' Trochoidal Wave 
Theory," covers the whole question of wave forms at sea. But it is at least 
a good working hypothesis for simple waves in very deep water, and has the 
advantage of covering all forms oetween the two *' limits" of trochoids, 
viz., the cycloid and the straight line, the last being, of course, smooth water. 

The centrifugal force is perpendicular to the wave surface at the crest, and 
acts directly in opposition to the universal gravity force, which we can never 
leave out of account. Whatever influence this may have in reducing the 
weight of the particles of wave water, it does not deflect them from the 
vertical line. At the wave hollow the centrifugal and gravity forces also act 
(this time together) in a vertical direction. In no other positions than wave 
crests and hollows does centrifugal force exert itself perpendicularly to the 
wave surface. In all other parts of the wave surface, its force acts more or 
less obliquely, and gravity, as it always does, acts vertically, the resultant of 
which two forces (together with any other less important yet possibly existing 
forces) is approximately square to the wave surface. And thus the original 
lines of buoyancy pressures, which were vertical in still water, are continually 
changing the direction of their lines of action in wave water. (Sec fig. 100.) 



kitoW fcftiA om amp. 




ROLLING. 157 



The short, dotted lines, perpendicular to the immersed surface of the vessel, 
indicate the water pressures. The longer dotted lines, approximately per- 
pendicular to the wave surface, indicate the direction in which the action of 
buoyancy is exerted. These lines likewise indicate the virtual upright. When 
a vessel floats with its deck parallel to the wave surface, the line of action 
through the centre of buoyancy passes through the centre of gravity, and no 
righting lever exists under such circumstances (see first position in the figure, 
and also the first position in fig. 99). 

Position 1 shows the vessel upright, when the hollow of the wave reaches 
her. The lines of action of gravity and buoyancy are vertical 
and coincide, and the vessel possesses no tendency whatever to 
incline to the one side or the other* 

Position 2. Here the wave has advanced and the vessel is upon the slope. 
The direction of the buoyant action has changed, and the line 
through the centre of buoyancy does not pass through the 
centre of gravity. The righting lever now existing (the distance 
between the parallel lines passing through 6 and G) tends to 
bring the vessoPs masts pei'pendicular to the wave surface. 

Position 3. The vessel is now upon the wave crest. Here she is still lagging 
behind in her efiForts to rear herself perpendicular to the wave 
surface, and instead of being upright she is considerably in- 
clined. The distance between the parallel lines through B and 
G indicates the righting lever. 

Position 4. Here the vessel is upon the other slope of the wave, having only 
succeeded in reaching the vertical position. Considerable right- 
ing lever exists, as shown, still tending to bring her perpendicular 
to the wave surface. 

Position 5. The righting moment produced in position 4 creates a momen- 
tum, which, by the time the vessel reaches the wave hollow 
(position 5), has carried her beyond the vertical — in this case 
the perpendicular to the wave surface. The righting lever is 
again indicated. 

The raft, being very stiff, and therefore much more rapid in its movements 
maintains a condition always perpendicular to the wave surface. 



168 KNOW YOUR OWN SHIP. 

In dealing with a cylinder of no stability, we must not forget 
that the least external effect of wind or water washing over it 
might make it revolve ; the only resistance offered to this would 
be the friction of the water on its immersed surface. In the 
instance we took as an example, we considered it as not affected 
by any external force, but simply under the influence of the 
unbroken wave water. Now a modem ship is neither like a 
raft nor a cylinder, yet it includes in some measure the quali- 
ties of both, and may approach either in behaviour. 

Ship, — Let us continue our experiment, and, placing an actual 
ship among waves, watch her behaviour (figs. 99, 100). If she is 
very stiff indeed — that is, has great metacentric height, with her 
still-water rolling period less than half that of the waves she is 
among, she will act very similarly to the raft, which makes two 
complete rolls on a single wave. Supposing her to be floating in 
the upright position, immediately the base of the wave reaches 
her, she will at once seek to keep her masts perpendicular to the 
wave surface. As the wave passes under her, she will reach, or 
approximately reach, her greatest angle of inclination on the 
steepest part of the wave-slope ; she will be upright at the 
summit, and again upright in the trough. She will, therefore, 
make two complete rolls in passing a complete wave (summit to 
summit). Her greatest angle will always occur approximately 
where the wave-slope is steepest. So that the danger in such a 
ship would lie not in capsizing, for she scarcely ever expends any 
of her stability, but owing to the rapidity of her movements, to 
shift the cargo, or strain her structure. 

Synohronism. — But let us suppose that our vessel is tender, 
possessing a small metacentric height and long rolling period. 
When the wave reaches her and passes underneath, she will 
endeavour, as did the other ship, to rear . herself perpendicularly 
to the wave surface. But we observed in our remarks upon 
rolling in still water that she moves slowly, and so she cannot 
keep up with the rapid motion of the wave, and falls behind. 
Thus, by the time the steepest part of the wave is under her, 
she is still at a considerable distance from that angle. Immedi- 
ately that point is passed, the less inclination of the wave, as the 
summit is approached, checks the heeling influence, and at the 
summit the tendency is to bring her to the upright again. 
However, here she is yet lagging behind the wave, having still 
some inclination. When the other slope of the wave is reached 
she has possibly just reached the upright, and, before she can 
heel far under its inclining influence to the other side, the 
trough is reached, where the tendency is to bring her to the 
upright. We see then, that, by her slower movements, she lags 



BOLLING. 159 

behind the wave, and never reaches the angle of the greatest 
wave-slope, and at the summit and the trough is generaUy 
still inchned, not having reached the upright. Taking two 
such ships upon a single wave, the stiff vessel with the great 
metacentric height will always reach greater angles of inclina- 
tion than the tender one with the small metacentric height, 
simply because, as we have shown, the stiff ship can better 
follow the angle of the wave ; while the tender one of slower 
motion cannot reach the greatest angle of the wave on the one 
side of the slope, while, after the wave has passed beneath her, 
the other slope tends to push her back, and heel her to the 
opposite side. But, although the passage of the first wave may 
not have the effect of producing any great angle of inclination, 
owing to the usually slower movement of the ship in comparison 
with the speed of the waves, or more properly speaking, the 
longer double roll jpenod to the wave period, it must be clear 
that a time may come when a ship may reach her greatest 
angle of inclination when the greatest angle of wave-slope 
reaches her. The result will then be, that a comparatively 
sudden additional impulse is given to the heeling of the vessel, 
and she will take an extraordinary, and what seamen have often 
called an unaccountable, lurch. Such a condition of waves and 
ship reaching their greatest angle of inclination at the same 
moment at regular intervals, is termed synchronising^ or in other 
words, keeping time, and the effect is to produce considerably 
greater angles of inclination in the ship than the steepest wave- 
slope. The worst case is that where the period of a ship's single 
roll is half that of the wave period, as 
under such circumstances the impulse is 
given on each wave, and. excessive rolling 
is naturally set up. This can be further 
illustrated by a simple pendulum (fig. 
101). 

Let us imagine that the pendulum has 
just swung out to almost its greatest 
angle of inclination in the direction of 
the arrow. Suppose it receive a sudden ^^^ loi.— Influence of 
impulse on the side B, it will naturally External Foeces on a 
be checked, and commence its return to Swinging Pendulum. 
the vertical position. But suppose, on 

the other hand, the impulse had been given on the side A, at 
the moment the pendulum reaches its greatest angle, when there 
is neither return nor outward motion. The result is that a slight 
impulse will considerably increase the extent of its outward move- 
ment, and produce a greater angle from the vertical. This is 




160 KNOW YOUR OWN SHIP. 

exactly what happens with a vessel whose period of roll synchron- 
ises with the wave period ; if a sudden impulse be given near the 
extremity of her outward motion, a considerable augmenting of 
the angle of heel will result. The eflfect is bad enough when the 
synchronism occurs periodically — that is, with a series of waves — 
but when it happens on every oscillation, the eflfect is still more 
excessive, and the motion experienced by the vessel is rapid and 
jerky, with the greater probability of producing dangerous results. 
Stiff vessels with quick periods of about four to six seconds, would 
be the most likely to develop such behaviour. Vessels of longer 
or shorter periods may destroy synchronism altogether in most 
cases. 

Were all sea waves of the same length, period, and height, it 
would be quite possible to design a warship or a yacht, whose 
equipped conditions are of an unvarying nature, to give a 
rolling period in still water which would produce great steadiness 
among waves. 

But sea waves, at different times and places, vary greatly in 
length, period, height, and character. Atlantic storm waves 
reach 500 feet and over in length from crest to crest, with 
periods of 9, 10, or 11 seconds, and heights of 28 feet and over, 
while in other localities the length may not be more than 200 or 
300 feet, with varying periods of 6 to 8 seconds, and height of 
about 12 feet. 

Effect of Loading on Behaviour. — As waves, therefore, vary, 
according to the locality, the force of the wind, etc., it must be 
fairly clear that to design either a warship or a yacht to behave 
always in the same manner among waves is impossible, for 
although it is not likely that vessels with long rolling periods 
will be -subject to heavy rolling, yet it is most probable that at 
some time they may fall in with waves which synchronise with 
their own period, and this inevitably produces heavy rolling. 
With merchant steamers the difficulty in producing steadiness is 
more marked than in any other case. In the first place, there 
is the difficulty, especially in coasting vessels, whose loading has 
to be rapidly conducted, with possibly part of the cargo arriving 
just before they sail, of obtaining a certain metacentric height 
which is known to have produced steadiness on a former occasion ; 
or, if the metacentric height is the same, considerable difference 
may have taken place in the positions of the weights of the cargo, 
not vertically, but out on each side from the centre line of the 
ship. 

This brings us to another very important point. While small 
metacentric height conduces to steadiness, the error must not be 
fallen into that this mode of procedure can always be carried out. 



ROLLING. 161 

So long as the levers of stability at considerable angles be good, 
and the range satisfactory, such a method is all very welL But 
in tender vessels with short levers and short range, as seen by 
curves Nos. 11, 12, 6, and 7, fig. 87, such a method is extremely 
dangerous, for should synchronism be set up, they may take an 
excessive roll and capsize altogether, so that it is evident some 
vessels need more metacentric height than others, in order to 
ensure safety, even though it produces more lively motions among 
waves.* 

Effect of Transverse Arrangement of "Weight on Rolling 
Motion. — A safe method which can be adopted to assist in 
producing steadiness in such a case, is to wing out the heavy 
weights of the cargo, on each side of the vessel, without altering 
their position vertically. Such an arrangement of cargo will 
have a steadying effect upon lively transverse motions, and, on 
the other hand, concentrating the weights in the middle line of 
the vessel would tend to increase the rapidity of the transverse 
rolling.! 

Alteration in Behaviour during a Voyage. — In ocean 
ships, whose loading is possibly not so hurried, or at any rate 
the nature of whose cargo is often understood beforehand, 
because it is all or nearly all alongside before commencing to 
load, it is certainly possible to so carry out this method when 
a knowledge of a ship's stability is understood, as to closely 
approximate to a particular metacentric height, and moreover 
to arrange the weights so as to be best fitted for steadiness. 

Supposing we have secured a certain metacentric height which 
has produced great steadiness even in a heavy sea, it is some- 
times found that this same vessel in a long, low ground swell of 
greater period, labours in a most extraordinary manner. Such 
is not an unknown experience to seamen, and the cause is simply 
due to the fact that the vessel has now fallen in with waves 
which synchronize with her own period. An instance bearing 
on this point was related to the author by a captain. Coming 
from the Mediterranean with a light cargo, he encountered 
heavy weather. His ship was naturally tender, and behaved 
splendidly for some time, but on approaching the Bay of Biscay, 

* It may here be Doted that it is utterly impossible to specify a meta- 
centric height adapted to all vessels. For vessels in the Royal Navy, it 
varies from 1 foot to 12 feet. In steam yachts 2'5 feet is probably an 
average ; in sailing ships 2 to 4 feet is common, and in passenger and cargo 
steamers it ranges from about 0*5 to about 3 feet. Shipbuilders with their 
wide experience of the various types of vessels are undoubtedly most capable 
of suggesting the best metacentric height for any particular condition of 
loading. The foregoing metacentric heights are only for loaded conditions. 

t See Appendix, 



162 KNOW YOU^ OWN SHIP. 

a long heavy swell set in, and the ship began to roll so heavily, 
especially at periodic intervals, that he imagined she would 
capsize altogether. He immediately set to work and filled one 
of the water ballast tanks, with the result that the vessel com- 
pletely altered in her behaviour, and again regained comparative 
steadiness. The ship had evidently fallen in with waves which 
synchronized with her own period, and caused the heavy rolling, 
but by filling a ballast tank the metacentric height w^as increased 
and the ship's period altered. Then, there being no longer 
synchronism, she steadied. Every seaman naturally learns from 
experience that where heavy rolling is suddenly set up, it can 
be modified by an alteration in the course or the speed. The 
reason is not far to seek. If the synchronism is produced by a 
beam sea, by changing the course more towards the waves, the 
apparent wave period is decreased, the crests being now passed 
more rapidly. By taking a course in an oblique direction, away 
from the direction at right angles to the waves, the wave period 
is increased, and in any other sea than one direct abeam, an 
increase in the speed without altering the course will decrease 
the wave period. Thus synchronism can be prevented either by 
altering the course or speed, and thereby altering the apparent 
period of the waves, or by altering the period of the ship through 
shifting weights in the ship. 

Synchronism is not always produced by a beam sea, for the 
sea coming in an oblique direction may cause the vessel's period 
to synchronize with the wave period, when no such result would 
have happened with a beam sea, and therefore such large angles 
of roll could not have been experienced. How to obviate this 
has just been mentioned — by changing the course or speed. To 
attempt to alter the ship's period by filling the water ballast 
tanks when rolling heavily is by no means a safe experiment, for 
the moment of the free water dashing from side to side before 
the tank is filled, may add to the angle of heel, instead of 
reducing it. We must now be able to see that great stability is 
not the best condition for a ship, for it will either make her 
movements exceedingly rapid, following, as in the case of the 
raft, the wave-slope, or, if not so stiffs, tending to produce 
synchronism, with consequent heavy rolling. 

The Metacentric Height. — The best vessel is undoubtedly 
the one with moderate metacentric height, good levers of stahility 
at considerable angles of inclination, and good range. She 
will probably thus be slow in her period, easy in her move- 
ments, and when not subject to synchronism (which she is less 
likely to be) will be comparatively steady among waves. 

To secure steadiness at the cost of small metacentric height, 



ROLLING. 163 

with short levers and range of stability, would only make disaster 
more probable. This is the very reason why a ship's officer 
should possess stability curves of his vessel in the various con- 
ditions under which she is likely to proceed at sea, from which 
he will undoubtedly be more able to intelligently manoeuvre the 
condition of his ship in order to produce seaworthiness. 

Could we imagine a vessel rolling among waves unresistedly 
(that is, without being subject to resistance from wind, immersed 
surface, or keel resistance of any sort), whose own period syn- 
chronized with that of the waves, the effect would be that the 
continued impulses given by the synchronizing waves would 
eventually capsize her, whatever might be her stability, just as 
a child's swing pushed synchronically would at last overset. 
These resistances have the same effect among wave water as 
when rolling in still water. There is one important point, how- 
ever, to be observed, and that is, the more rapid the motions of 
the vessel the more resistance is offered. And thus, upon a 
vessel whose period synchronizes with the wave period, when 
she begins to attain large angles of heel and great rapidity of 
motion, the various resistances grow in proportion until a point 
may be reached where the effect of these resistances is just 
sufficient to prevent greater oscillation being attained, and cap- 
sizing is also averted. Thus, where synchronism produces great 
angles of oscillation, it does not follow that the ship will capsize, 
except in unusual cases where the range of stability is very short. 
The great and important value of bilge keels in offering resist- 
ance and reducing rolling, has already been shown from Mr 
Froude's experiments. These will produce good results upon 
large ships, but the effect is still more apparent upon small 
vessels of quick period. 

Fore and Aft Motions. — Thus far our remarks have been 
confined entirely to transverse stability and behaviour relatively 
to transverse motions at sea, simply because that it is in these 
directions that danger is most likely to occur. Could we heel 
our ship in every possible way it would be found that she 
possessed least stiffness or stability when inclined transversely 
than in any other direction, and that her transverse metacentric 
height is the smallest possible. Thus, on heeling in any skew 
direction, more stability is developed, and most of all when 
inclined longitudinally (pitching). In ordinary types of vessels 
it is, therefore, only possible for them to capsize transversely, 
unless it happens that, through damage and the admission of 
water, the loss of buoyancy at either end is so great as to cause 
the vessel to go down by head or stem, as the case may be. 
This explains why it is only necessary to be- provided with 



164 KNOW YOUR OWN SHIP. 

curves of transverse stability, and to be thoroughly aware of the 
vessels condition in this respect. The greatness of longitudinal 
metacentric height will be obvious when it is observed that the 
moment of inertia of the waterplane about a transverse axis must 
be immensely increased beyond that for a longitudinal axis, 
simply because what was formerly considered as beam in the 
formula for the transverse metacentre becomes length, and the 
length becomes beam. 

The principles which govern transverse behaviour apply in a 
similar manner when considering the longitudinal motions of a 
ship, though here again the design may exercise much influence 
in the production of objectionable qualities in behaviour. For 
example, take an ill-designed vessel considerably full on the load 
waterline aft, but fined away forward with sides almost vertical 
to the gunwale. Such a vessel will be admirably adapted for 
diving into the sea and shipping huge volumes of water on her 
deck, with her stern probably high and dry. However, it must 
not by any means be inferred that the load waterline forward 
should be bluff* or even identical with the after end, but certainly 
where any degree of comfort is desired, there should be some 
reasonable approach to equality. A vessel, very fine under 
water, may be considerably improved by giving her reasonable 
flam * or flare above the waterline, the additional buoyancy pro- 
duced by which forms a valuable check upon diving. 

But we have also noticed that winging out the weights trans- 
versely from the centre line produces slower rolling motion, that 
concentrating them on the centre line creates greater liveliness, 
and, moreover, that the latter result is always produced by a 
large metacentric height, and steadiness by a moderate meta- 
centric height. 

Fore and Aft Arrangement of Weights. — With the enor- 
mous longitudinal metacentric height — that is to say, length 
metacentric height, not beam metacentric height — possessed by 
most vessels, it is impossible to make any visible effect upon 
the longitudinal motions through this agent, for even were it 
possible to reduce or increase it by a few feet, the comparative 
difference would be exceedingly slight. Moreover, such altera- 
tion in the position of the centre of gravity might seriously 
imperil the safety of the vessel transversely. Thus, the oaly 
alternative is to influence longitudinal motion by a proper adjust- 
ment of the heavy weights of the cargo in a fore and aft direction. 
If liveliness is required — that is, quick rising motion — they should 

* By flam is meant exactly the opposite to '* tumble home." It is most 
noticeable at the bow of a ship, where her sides slant outwards, greatly 
increasing her beam above the load waterline. 



ROLLING. 165 

be stowed nearest to midships ; if a slower movement is required 
they should be spread out longitudinally (that is to say, more 
fore and aft). But it must not be forgotten that placing heavy 
weights at the extremities of a vessel has the tendency to exces- 
sively strain the structure when subject to the varying support 
of wave water, and also to some extent when lying at rest in 
still water. 



166 KNOW YOUR OWN SHIP. 



CHAPTEK VI. (Section III.) 

BALLASTING. 

Contents. — Similar Metacentric Heights at Different Draughts — "Wind 
Pressure— Amount and Arrangement of Ballast — Means to Prevent 
Shifting of Ballast — Water Ballast — Trimming Tanks — Inadaptability 
of Double Bottom Tanks alone to Provide an Efficient Means of Ballasting 
— Considerations upon the Height of the Transverse Metacentre between 
the Light and Load Draughts, and Effect upon Stability in Ballast — 
Unmanageableness in Ballast — Minimum Draught in Ballast — ^Arrange- 
ment of Ballast. 

Ballasting. — The number of losses and disasters happening 
annually, not only to old, but often to fine new ships when in 
ballast, abundantly proves that something is wrong. This is 
all the more manifest from the random way in which ballast is 
often thrown into a ship. One man considers 400 tons sufficient, 
and another, 800 tons for the same ship, and all pitched into the 
hold. Both cannot be right, since both methods cannot produce 
similar results. One is either dangerously stiff, conducing to 
heavy rolling and tending to shift the ballast, or the other is too 
tender with too small righting moments. 

Before ballasting can be intelligently carried out, it is neces- 
sary that a few important facts be kept in mind. 

1. That metacentric height alone is no gitarantee for a vessel's 
stability. 

2. That freeboard alone is no safeguard. 

3. That although a certain metacentric height on one occasion 
may be very good for a vessel at a particular draught, the same 
metacentric height would be unsafe at a different draught, and 
even if it were possible to get the same lengths of righting levers 
at a certain angle of inclination at light and load draughts, the 
righting moments in each case would be immensely different. 

Similar Metacentric Heights at Different Draughts. — 
Reference to curves Nos. 5 and 18 (fig. 87) will considerably 
help in illustrating these points. Curve 5 is for a box 
vessel 100 feet long, 30 feet broad, 10 feet draught, and 5 feet 
freeboard in the load condition, with a metacentric height of 6*2 
feet, the centre of gravity being 6*3 feet from the bottom of the 
box. Curve 18 is for a box vessel 100 feet long, 30 feet broad. 



BALLASTING. 167 

4 feet draught, and 16 feet freeboard in the light condition, with 
a metacentric height of 6*2 feet, the centre of gravity being 14*5 
feet from the bottom of the box. 

Taking metacentric height and freeboard as the only guides, 
the latter vessel should have by far the greatest stability. 
A comparison of the curves contradicts such a conclusion, and 
shows that the higher the centre of gravity is with a certain 
metacentric height and freeboard, the smaller will the angle be 
at which the vertical line through the centre of buoyancy inter- 
sects the centre line of the ship below the centre of gravity, hence 
the increased range of curve No. 5. Fig. 90 is the stability 
curve for a sailing barque in the light condition, with 112 tons of 
ballast aboard. The length is 270 feet, the breadth 41 feet, and 
the freeboard 17 J feet, with a metacentric height of 2*9 feet and 
a displacement of 1390 tons. The maximum lever of stability is 
0*69 at 18° of inclination, and the righting moment 1390x0*69 
= 959 foot-tons. Moreover, the stability vanishes altogether at 
the comparatively small angle of 34°. 

Wind Pressure. — Both the maximum lever and range are 
exceedingly small for a heavily-rigged vessel with large sail area, 
and the effect of a sudden squall of wind with much sail set is 
easily perceived. In the loaded condition, however, with only 5J 
feet freeboard, 4000 tons displacement, and a much lower centre 
of gravity with the same metacentric height, this same vessel 
would have longer levers and much greater moment, as well as 
greater range of stability. 

Amount and Arrangement of Ballast. — Now let us take a 
practical view of the process of ballasting a ship, and suppose that 
as master we are told by the naval architect or shipbuilder that a 
metacentric height of 3 feet in the loaded condition, which gives 
a displacement of 4000 tons, will put our ship in an excellently 
seaworthy condition. 

In the light condition, however, by placing 500 tons of ballast 
in the hold, the same metacentric height is secured with a total 
displacement of 2000 tons. 

Heeled to an angle of 10°, the righting lever will be — 

G M X sine of angle = 3 x 0*1736 = 0*52 foot. 

As regards length of lever at this angle of inclination, the 
vessels are practically identical at both these draughts. The 
righting moment, however, is lever multiplied by displacement. 
Thus, at the load draught the righting moment is 0*52 x 4000 = 
2080 foot-tons ; at the light draught the righting moment is 0*52 
X 2000= 1040 foot-tons — only one-half the loaded righting 
moment. It is clear, then, that with equal sail area and equal 



168 KNOW YOUR OWN SHIP. 

wind pressure, the vessel in the light condition would heel to a 
much greater angle than in the load condition ; moreover, the 
effect of a sudden squall of wind will produce about double the 
angle of inclination which would otherwise be reached in steady 
heeling. There is always greatest motion at and near the surface 
of wave water, so that the lighter the vessel, the more on the 
surface she will float and be subject to the influence of waves and 
wind. Possessing great stiffness under such conditions, the more 
excessive wull be the rolling. Righting lever alone, then, does 
not provide righting moment, but lever multiplied by displace- 
ment. To get moment without excessive metacentric height, 
there is no alternative but to considerably immerse the vessel in 
order to get displacement. 

Understanding this, we proceed to put ballast into our vessel. 
Supposing the ballast to be sand, it would probably be found that 
if it were all poured into the bottom of the hold, by the time 
the ship was sufficiently immersed excessive stiffness would be 
set up. 

This method, therefore, cannot be adopted. We know that to 
reduce metacentric height, low weights must be raised so as to 
lessen the distance between the metacentre and the centre of 
gravity. Part of the ballast, therefore, would require to be 
carried in the 'tween decks. But here, again, a difficulty arises 
in many cases, where a vessel with good beam, and a depth 
to require two tiers of beams instead of having a laid deck on the 
lower tier, this lower tier is made extra strong and the beams are 
widely spaced, making it impossible to carry ballast higher than 
the hold. What is to be done ? Very often nothing is done, and 
only one or two conclusions can be arrived at, either the expense 
of making provision for efficient ballasting is considered too much 
for some owners whose vessels are amply covered by insurance, or 
else out of pure ignorance of the mode of ballasting to ensure 
safety, this subject receives no consideration. One thing which 
could be done under such circumstances to produce excellent 
results, would be to build two tanks at the middle of the length 
of the vessel, one on each side, between the hold beams and upper 
deck beams, to contain, say, about 50 tons each, or, altogether, 
100 tons. JEach tank w^ould, therefore, require to be about 30 feet 
long, 8J feet broad, and 7 feet deep. Especially if the ship were 
fitted with water ballast tanks in the bottom, the size of these 
upper tanks could be fixed to a nicety; but in any case, the 
shipbuilder could supply the information as to the exact amount 
of hold ballast to be used. 

This would reduce the stiffness by raising the centre of gravity, 
but furthermore, having these weights " winged " out to the ship's 



BALLASTING. 169 

sides, would still more conduce to steadiness. The application is, 
therefore, twofold. 

This method entails the expense of the plating, additional 
beams, and pillars for supporting the tanks. Expense is always 
objectionable, but there is the choice between possible and prob- 
able loss of life through ignorance or carelessness in ballasting, 
not to mention the ship ; and the comparatively small additional 
cost upon the vessel while building. When loading cargo, and 
these ballast tanks are not required, the space could conveniently 
be used for cargo also, if a hatch be made on the deck above them. 

The same idea could be carried out by constructing these 
ballast spaces of wood battens, instead of iron plating, and using 
earth or sand ballast. The former method is, however, preferable, 
and economical, since the water could be run out by means of a 
cock on the ship's side. 

Means to Prevent Shifting of Ballast. — The other great 
point in ballasting ships is to see that the ballast is secured so as 
to render the likelihood of disaster from shifting impossible. If 
it be water ballast confined in a tank, it is all right if the tanks 
are full, for it must be remembered, as will be pointed out in the 
remarks upon " water in the interior of a vessel," free water may 
create a list if the vessel is inclined to be tender. But supposing 
the ballast to be sand in the hold, great pre'caution should be 
taken to make it immovable as far as possible. The value of 
shifting boards as applied to cargo applies equally to this also, for, 
after all, ballasting is just a form of loading. 

Another method sometimes adopted is to cover the surface of 
the ballast with boards and shore them down. This is all w^ell 
enough if the covering and shoring is thoroughly carried out, 
rendering no possibility of any ballast shifting, or finding its way 
between the boards or uncovered spaces, for where such is possible 
the precaution is useless, as the ballast will all the more readily 
and easily relieve itself from its confinement. 

Water Ballast. — Among a host of important considerations in 
designing a vessel, draught is one which ever demands careful 
attention. Limitations upon the depths of dock entrances, 
harbours, rivers, etc., have in turn fixed the limits of depth and 
draught for vessels. And thus, in many cases, while owners have 
vastly increased the size of their vessels to carry a greater dead- 
weight, the length and breadth almost entirely have furnished the 
additional capacity, little alteration having taken place in the depth. 

While earth, sand, or stone possesses certain advantages as 
agents in ballasting, the cost entailed in loading and discharging 
hundreds of tons of these materials often causes both serious loss 
of time and expense. The advantage they possess is that they 



170 KNOW YOUR OWN SHIP. 

can be laid wherever desired in order to secure a certain condition 
of ballasting — on the deck, in the 'tween decks, or in the hold 
with perhaps, in some cases, precautions to prevent shifting as 
previously pointed out. But with the adoption of iron for the 
construction of ships, it was found that the bottom of the vessel 
could be constructed so that while providing adequate and ample 
strength, it might form at the same time a most convenient and 
economical means of carrying water for ballast, for trimming 
purposes, and for adjusting the stability under certain conditions, 
not to mention the further important advantage of providing an 
inner bottom, which has proved the salvation of many a ship, 
when, by some means or other, the outer bottom has been so 
damaged as to admit water. No doubt the division of this water- 
tight space into separate watertight compartments gave to them 
the more correct name of Trimming Tanks. For this purpose 
they are admirably adapted, and may be fitted into almost any 
type of cargo or passenger vessel with decided advantage. But 
when these trimming tanks are used apparently with the expecta- 
tion that they will also serve as an efficient means of ballasting, 
one hesitates before calling them a universal success. 

In these days of fluctuating freights, many vessels, especially 
of the tramp class, find themselves without cargoes. To proceed 
to sea with an empty tramp would be to court disaster. As 
seamen know from experience, the enormous freeboard, slight 
immersion, and sometimes deficient stability, would make these 
vessels both extremely dangerous and utterly unmanageable in 
bad weather. Ballast, therefore, becomes an absolute necessity. 
And the tempting convenience of double bottom tanks has caused 
them to be so widely adopted that their primary use has come to 
be for ballasting purposes. A variety of forms of double bottom 
ballast tanks have been built, but the system now generally 
adopted is that known as the cellular double bottom. See fig. 55. 

Inadaptability of Double Bottom Tanks to Provide an 
Efficient Means of Ballasting. — And yet after we have got 
this apparently commendable system of ballasting fitted into the 
modern tramp, to whose lot it oftenest falls to do long, and even 
Atlantic runs, in ballast, together with possibly a few hundred 
tons of coal in bunkers, officers on board many of these vessels 
complain of the miserable existence they endure in bad weather, 
owing to the heavy rolling, disregard of helm, and general un- 
manageableness of their ships. Something must be wrong some- 
where, and as this double bottom tank does not produce the 
results required, we had better examine the basis upon which it 
finds its way into a ship. 

Taking the specification of an ordinary cargo vessel which has 



BALLASTING. 171 

to be built to Class 100 Al at Lloyd's, we are pretty sure in most 
cases to find the phrase " cellular double bottom all fore and aft 
for water ballast to Lloyd's requirements." But what does 
"Lloyd's requirements" mean? Kequirements for ballasting? 
No. Ballasting lies entirely outside their province. Neither 
Lloyd's nor any other of the societies for the registry and classifi- 
cation of vessels, have any requirements for ballasting. Ballasting 
is a feature in the ship design, and the owner, or whomsoever he 
appoints to design his vessel, is solely responsible for the ballast- 
ing arrangements. The owner may have practically whatever 
design of vessel he likes, with whatever arrangement for ballasting 
he chooses, such as, cellular double bottoms extending fore and 
aft, or, through part of the length ; deep tanks ; peak tanks ; 
hold, or part of hold spaces ; bunker spaces, etc. ; providing that, 
so long as his vessel is built to the standards of strength fixed by 
these societies, and the spaces intended for the carriage of water 
as ballast are structurally to their satisfaction, the vessel will be 
classed with a minimum freeboard. 

A vessel may be built without any arrangement whatever for 
ballasting purposes, and owing to her particular mode of con- 
struction, it might be absolutely impossible to carry water as 
ballast, yet she may still be perfectly eligible for the highest 
class, and fully satisfy the requirements of the Board of Trade. 
And when a double bottom system of construction is adopted, 
it is never asserted that such space is adequate and properly 
adjusted for the efficient ballasting of a ship, but it is simply 
offered as a means of carrying water for ballast or for trimming 
purposes, or for fresh water for the boilers, or for whatever 
purpose owners may find it useful. 

It would have been unnecessary to go into this detail were it 
not for the fact that it is evidently very often and absurdly 
assumed that because the double bottom is built to Lloyd's 
requirements, the arrangement for ballasting is both proper and 
sufficient. This is proved by the fact that large numbers of 
vessels are constantly proceeding to sea dependent only upon 
this ballast, together with a greater or less amount of bunker 
coal on board. We have only to observe the method followed 
in, say, Lloyd's rules, for arriving at the dimensions of cellular 
double-bottom ballast tanks, to see that such could never be 
intended as a competent mode of ballasting the various types 
and differently proportioned cargo vessels. 

Let us take an ordinary flush deck type of tramp steamer with 
poop, bridge, and forecastle, built of steel to the three-deck rule, 
and Classed 100 Al at Lloyd's. The dimensions are : length, 
350 ft. ; breadth, mid., 45 ft. ; depth, mid., 29 ft. 



172 KNOW YOUR OWN SHIP. 

In order to find the particulars for the construction of the 
ballast tank, we are instructed in Lloyd's rules to proceed as 
follows : — 

Find the 2nd numeral for scantling, as described on page 63. 
For this vessel it is 32,506. Turning to Lloyd's rules we find in 
a table relating to double bottoms a graduated list of similar 
numerals. Tracing down this table, we arrive at the particulars 
for tanks for vessels whose numerals are between 28,000 and 
33,000. Here we see that the depth of the centre girder is 3' 6", 
and the minimum breadth of the tank side is 2' 4". 

The depth of the centre girder, or centre keelson, being de- 
termined — which, by tlie way, is one of the most important items 
in the structural strength of the bottom of the ship, since it regu- 
lates the depth of the floors, and, to a large extent, the other side 
girders in the tank also — the plating for the inner bottom is laid 
over the top of these, and riveted, caulked, and made watertight. 
And thus we have our ballast tank to Lloyd's requirements. 

In fig. 102, curve 1 is for a modem beamy cargo vessel and 
curve 2 for a vessel of the older and narrower type. 

We observe, that at light draughts the metacentre is at the 
greatest heights above the keel, simply because the extreme 
fulness of the bottom of especially the beamy class of vessels 
causes them to float at comparatively very light draughts with 
very large moment of inertia of the waterplane in comparison with 
the displacement at the same draught. It is found, however, that 
by increasing the displacement the metacentre rapidly lowers, the 
explanation being that the successive waterplanes above the light 
draught increase very slightly in fulness, and consequently the 
moment of inertia also is only slightly increased. The displace- 
ment, on the other hand, increases much more rapidly in propor- 
tion, and thus : — 

Sliffhtly increased Moment of Inertia , 

— 2 — I = a very much 

Greatly increased displacement in cubic feet 
lower metacentre, notwithstanding the fact that with every increase 
in draught, the centre of buoyancy has risen, and tended to keep 
up the metacentre. 

The downward tendency of the metacentre continues until, as 
the vessel approaches her load draught, the ratio between the 
moment of inertia of the lower waterplanes and the displacement, 
and the moment of inertia and the displacement at the upper 
waterplanes, has so altered, that the steady rising of the centre of 
buoyancy has at last the effect of causing the metacentre to take 
an upw^ard course again {see curves 1 and 2). Here, then, in 
these natural movements of the metacentre it seems we have th^ 
secret of correct ballasting. 



173 

With the deductions and inferences we have made from these 
simple considerations of the naetacenlre, we shall now revert to 
our cellular double-hot torn tanks, and examine the complaints 
lodfjed against vessels ballasted by means of them only. 

First, then, mauy of them are heavy rollers, and cause estreme 





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No. 1 Steamer, 360' x i7' Mid. x 28' Mid. Light draught, S' 6'. 

Metacentre, 25' S" above keel. 

No. 2 Steamer, 376' x 13' Mid. x 29' 1° Mid. Light draught, 12' 11". 

Metoceotre, IS' 7}" above keel. 

Fia. 102. — Curves of TniNsVEHSK Mbtacentbeb. 

discomfort to those on board, in addition to severe straining to the 
vessels themselves. Some of the narrower types of cargo vesacla 
(notaljly older ones), have extremely little metacentric height, and 
in some cases actually a negative metacentric height in the light 
condition. (Compare heights of metacentre in light condition, 
No8. 1 and 2, tig. 102.) By fiUing the double-bottom ballast 



KNOW TOUR OWN SHIP. 





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BALLASTING. 175 

tanks, a decidedly positive metacentric height is obtained, which 
possibly is not excessive, and these vessels are known as steadier 
and better behaved at sea. But in recent years, considerable 
additions, amounting to 2, 3, 4 feet, and more, have been made 
to the beams of vessels with the corresponding increase in the pro- 
portion of beam to depth and draught. The result is, that 
though in both narrow and beamy vessels the centre of gravity 
may be at the same height above the keel, the metacentre of the 
broad vessel will be higher, and the metacentric height will be 
greater, and some of these vessels are actually stiff and stand up- 
right in perfect safety in a light condition. When proceeding to 
sea light, the ballast tanks are filled ; the centre of gravity is thus 
considerably lowered, and the naturally large metacentric height 
is slightly, if at all, diminished. It will be remembered that the 
metacentre lowers with increasing draught more rapidly than in 
narrower vessels. Fig. 102 illustrates such a comparison. Many 
of these modem beamy vessels are abnormally stiff, and as a 
result earn the reputation of being unmistakably lively. 

These remarks upon the metacentre may be further illustrated 
by referring to fig. 103. Here we have a number of curves of 
stability showing righting arms up to 90° of inclination. 

Curve 1 is for a steamer, 376' x 43' x 29' 1", floating empty with 
'78 of a foot metacentric height. This may be taken as a fair 
representative of the narrower type, the proportion of depth to 
breadth being '677. Unfortunately, we have no curve showing the 
stability of the vessel in ballast. Eut probably with ballast tanks 
and bunkers full, she would have approximately 2' 6" metacentric 
height which, judging by the curve for the light condition, would 
provide ample righting moment at large angles of inclination. 

With this curve compare No. 2, which is for a vessel 302' x 40' 6" 
X 24' 11". Here the proportion of depth to breadth is 'GIS, and 
the metacentric height 7*3 feet emptyj and also compare No. 3, 
which is for a vessel 360' x 48' x 27' 3". The proportion of depth 
to breadth is '568, and the metacentric height 11*09 feet, empty. 
The curves for these two vessels are fair representatives of a large 
number of the more modem beamy cargo vessels. With ballast 
tanks and bunkers full these two latter vessels have 5*63 and 8*45 
feet metacentric height respectively {see curves 4 and 5), and with 
bunker coal consumed and ballast tanks full, 7*15 and 10*83 feet 
metacentric height respectively. {See curves 6 and 7.) It is 
scarcely necessary to say that such metacentric heights as these 
indicate enormous stiffness, the effect of which quality is well 
known to seamen. As already stated, 7*3 feet is the metacentric 
height for the 302 feet vessel light, and yet after the double- 
bottom ballast tanks have been filled, and this large weight placed 



176 KNOW YOUR OWN SHIP. 

in the lowest possible position, the metacentric height is 7*15 feet, 
actually less than for the light condition. 

It is evident then, that, though the centre of gravity must have 
lowered considerably, the metacentre has lowered a still greater 
distance. With both ballast tanks and bunkers full, the metacentric 
height is only 5*63 feet, owing probably to the fact that, the 
bunkers being situated considerably higher than the water ballast, 
the centre of gravity has not lowered very much, if at all, while 
the metacentre, within these limits of draught, continues to 
descend very rapidly for beamy vessels. These remarks apply 
also to the 360 feet vessel, and an examination of the metacentric 
heights for corresponding conditions will show similar results. 

A much more marked difference is found in dealing in like 
manner with the 376 feet vessel. To begin with, the metacentre 
is within a foot or so of its lowest position at the light draught 
(see curve 2, fig. 102), and the filling of ballast tanks could 
not fail to lower the centre of gravity to such an extent as to 
produce a greater metacentric height. As already approximated, 
the metacentric height would be about 2*5 feet, and the curve 
of stability would rise much more steeply and produce longer 
righting arms. 

We may also notice here that though the metacentric heights 
and freeboards of both the 302 and the 360 feet vessels are 
reduced by the filling of ballast tanks and bunkers, yet, owing to 
the lowered centre of gravity, the righting arms are less for small 
angles of inclination, as indicated by the reduced metacentric 
height, and greater at larger angles of inclination. 

Another complaint, especially against tramps in ordinary ballast, 
is that of unmanageableness. No one would doubt the validity of 
such an accusation against a ship sent to sea light without ballast. 
But when properly ballasted surely a better state of affairs ought 
to exist. As an example upon which to work, let us take a cargo 
steamer whose deadweight capacity is 5800 tons. When fuUy 
loaded, the freeboard is 5 feet. The cellular double bottom tank 
has capacity for 900 tons of water, which is only about one-sixth 
of the total deadweight. To this, say, 300 tons of coal are put on 
board for bunker use. This gives a total of 1200 tons of dead- 
weight on board in ballast sea-going condition, one-fifth of the 
maximum deadweight. The draught is now 11' 6" on even keel, 
against 23' 0" in loaded condition, and the freeboard is 16' 6" 
against 5' 0". The propeller is slightly more than one-half 
immersed in still water against more than total immersion w^hen at 
load draught. Assuming her to be an ordinary full type cargo 
vessel with a 10-knot speed and considerable stiffness in ballast, 
she both rolls and pitches. The propeller in the best condition is 



BALLASTING. 177 

only partly immersed, and during her lively movements is subject 
to intervals of immersion and emersion. In her pitching movements, 
her often massive box-shaped fore end lends little assistance in 
making headway, but is continually thumping against walls of water, 
and the vessel actually experiences greater head resistance com- 
paratively than she does in the fully loaded condition. There is, 
moreover, less expenditure of propeller power in actually driving 
her. There is the sudden shock produced by the propeller blades 
striking the water after racing in mid-air, which is no doubt the 
cause of what has become quite a frequent occurrence, viz., the 
loss of propellers and the breaking of shafts. The rudder also adds 
its decreased efficiency through decreased speed and periods of 
emersion. Moreover, the huge freeboard, together with all 
erections — poops, bridges, forecastles, deckhouses, etc., — exposed 
to the force of a gale, with little or no keel resistance where a flat 
plate keel is used, introduces more or less leeway into the category 
of grievances, and where, as in some cases, the speed has become 
an unknown quantity, actual drifting is a consequent result. To 
reduce part of these ill features, after peak tanks have been fitted 
in many vessels. By this means both propeller and rudder are 
kept at greater immersion, but while the mean draught may 
have been increased an inch or two, the fore end of the vessel has 
suffered in emersion, and in attempting to steam with the wind 
abeam, the effect in causing the vesseFs head to fall off will be 
obvious. 

Every seaman knows that the cure for excessive stiffness (large 
metacentric height) is to raise weight already on board, or add 
top weight, and thus raise the centre of gravity. Suppose the 
first of these methods to be adopted. Instead of having a cellu 
lar double-bottom tank throughout the length, let it only extend 
over part of the bottom, and let the difference of the weight be 
placed, say, in a part of the 'tween decks arranged for water 
ballast. By such means we can arrive at practically whatever 
metacentric height w^e desire. But this is sometimes rather a 
dangerous experiment to make, and, as already pointed out, more 
especially so in sailing-ships, for in securing what may appear a 
desirable metacentric height we may rob our vessel of stability 
most seriously, when she heels to considerable angles of inclination. 

Going back to our curve of metacentres, No. 1, fig. 102, we 
observed that the metacentre is very high at light draughts. To 
attempt to approach such heights of metacentre with the centre of 
gravity by raising ballast in order to make the ship easy, would 
only increase the possibility of disaster. Every upward movement 
of the centre of gravity shortens both the lengths of the righting 
arms and the extent of the range of stability. So that by the 

M 



178 KNOW YOUR OWN SHIP. 

time we have so raised the ballast as to produce a moderate and 
desirable metacentric height, it is possible that the result is an 
unseaworthy ship, that is, a ship with a good metacentric height 
under other conditions, but with too little reserve stability at 
possible angles of inclination. For be it remembered that most 
carefully designed vessels may at times fall in with such a con- 
dition of sea as to produce lurching to considerable angles of 
inclination. It will easily be seen, then, how dangerous it might 
be in the case of a beamy ship, if small metacentric height were 
procured at the cost of decreased range and righting arms (fig. 104). 
It is therefore evident, particularly in the case of beamy ships 
floating at light draughts, with the usual amount of water ballast, 
that there is no choice, in order to ensure safety, but to accept 
larger metacentric height than required at load draught, which, 
moreover, cannot be averted by the ordinary double-bottom ballast 
arrangement, and in a spirit of resignation to put up with the rolling 
and other accompanying consequences. 

To produce safe and desirable results more ballast than is pro- 
vided by the usual double bottom is required, not necessarily to 
either raise or lower the centre of gravity to any great extent, if 
at all, but rather to further immerse the vessel. Why ? Simply 
because, as we have previously seen, by increasing the displace- 
ment, the metacentre rapidly lowers, and by this manipulation of 
the metacentre, we are relieved from indulging in any dangerous 
experiment of raising the centre of gravity to a height such as 
might produce disastrous results under the effect of heavy rolling 
or lurching. 

By placing more ballast on board (increasing displacement), a 
safe compromise is effected between the metacentre and the centre 
of gravity. Moderate metacentric height with the centre of 
gravity in the lowest possible position will give the best results, 
for by this means a slow and easy rolling period may be obtained, 
combined with ample righting moment at large angles of inclina- 
tion and sufficient range. This desirable condition could never be 
attained by the usual method of only building tanks ^long the 
bottom, varying from 3 to 4 feet in depth, as per Lloyd's rules. 
Nor yet could it be accomplished if these tanks were increased to 
twice their depth, which on no account could be advisable. For 
though the more than doubled quantity of ballast would have 
the effect of increasing the draught and the displacement, and thus 
inevitably bringing down the metacentre, no compromise has been 
made on the part of the centre of gravity, it having receded into a 
lower position. 

That more ballast is required to make both behaviour and 
manageableness more satisfactory features many owners are 



BALLASIIHG. 




180 KNOW TOUR OWN SHIP. 

perfectly aware, and in their specifications for new vessels they 
have stipulated that deep tanks of some sort should he fitted in 
some particular position in their ships. But even these have 
not in all cases given such results as were expected. It has been 
stated by some of those who have adopted them that the ships 
behaved little better, and the tanks were often a source of trouble, 
on account of leakage. 

There is nothing very astounding in the fact that many ships 
behave little better with such arrangement, simply because it is 
fitted on much the same principle as the average stevedore loads 
a ship he knows little about. In some cases these ships are almost 
as stiff as when depending only upon double-bottom ballast, and 
their behaviour at sea shows little, if any, improvement. 

The trouble of leakage has very often been proved to be the 
outcome of pure carelessness or ignorance. Instead of the tanks 
being filled to the uttermost, empty spaces have been left at the 
top, and, with a rolling ship, it does not require a very large 
endowment of common sense to foresee what would happen with 
so large a quantity of free water. An argument against these 
tanks has been brought forward to the effect that it is difl&cult to 
keep them thoroughly watertight, owing to the numerous severe 
strains borne by a ship in ' her rolling and pitching movements. 
A similar argument might apply to fore and after peak tanks, in 
which localities very severe strains are experienced, and yet these 
tanks can be kept watertight. Where outrageous proportions of 
depth and breadth to length are adopted, such working might be 
experienced as to make watertightness a doubtful quality, but in 
the ordinary type of cargo vessel, with sound workmanship and 
proper strengthening, there ought to be no special difficulty. 

Minimum Seagoing Draught. — The important questions 
then are. How much water ballast should be carried, and where 
should it be placed ? As previously stated, it is desirable to get the 
centre of gravity into the lowest possible position compatible with 
a moderate metacentric height. Ketuming again to the curves 
of metacentres, fig. 102, No. 1, for the beamy ship, shows that 
the metacentre is over 25 feet above the keel at light draught. 
With increasing draught it lowers, until, at about 18 feet draught, 
it reaches its lowest position. Here, then, is probably the ideal 
draught at which to fix the metacentric height. At no other 
draught could tenderness — small metacentric height — be obtained 
with greater safety with its accompanying easy rolling motion than 
at this draught. 

The centre of gravity is in the lowest possible position for such 
a condition with ample freeboard, 5 feet more than at load 
draught. The curve of stability would rise gently at firsts and at 



BALLASTING. 



181 




T 




m 



T 









^^m 




o 






9i 



CO 



182 



KNOW tOtJft OWN SHll*. 




90' 



Scale of Degrees. 



Curves of stability for a steamer. Length, 302 feet ; beam, 40 feet 6 inches ; depth 
mid., 24 feet 11 inches. Load displacement, 5183 tons. Freeboard, loaded condition 
F = 4 feet 10^ inches. Poop, bridge, and forecastle. 

Ship Complete— Steam up. 



• 
CD 
fl 
O 

...4 

a 
o 
O 

A 
B 
C 
D 
E 

F 
G 

H 


Bunker 

Coal, Stores, 

and Fresh 

Water. 


Water 
Ballast. 


Cargo. 


Maximum Stability. 


Height of 

Metacentre 

above Centre 

of Gravity. 


Degrees. 


Righting 
Lever. 


out. 
in. 
out. 
in. 
out. 

in. 
out. 

in. 


out. 

in. 

out. 

>> 
>» 


nil. 

}) 

)) 
n 

Homogeneous cargo 

at 48 cub. ft. per ton. 

ditto. 

Coal cargo at 

45 cub. ft. per ton, 

ditto. 


45 
46 
58 
57 
53 

50 
55 

52 


Feet. 
3-31 
2-68 
5-58 
4-77 
1-85 

1-45 
2-22 

1-78 


Feet. 
7-30 
4-92 
7-16 
5-63 
2-16 

1-99 
2-62 

2-43 



Condition F loaded with Homogeneous Cajeloo. 







Upright. 13^" IncUnation. 

Deck edge 
immersed. 



50° Inclination. 93° Inclination. 
Maximum Vanishing 



stability. 



point. 



Fig. 106.— Curves of Stability for a Steamer in Various 
Conditions of Ballasting and Loading, 



BALLASTING. 



183 




oor 



SoALE OF Degrees. 



Curves of stability for a steamer. Length, 360 feet ; beam, 48 feet ; depth mid., 
27 feet 3 inches. Load displacement, 8050 tons. Freeboard, loaded condition F = 5 feet 
5 inches. Poop, bridge, and forecastle. 

Ship Complete — Steam up. 



• 

£3 


bunker 






Maximmn Stability. 


^ll^ 


•W^ 


Coal. Stores. 


Water 








Height 

Metacei 

above Ce 

of Grav] 




and Fresh 


Ballast. 


Cargo. 






a 
o 


Water. 






Degrees. 


Righting 
Lever. 








Feet. 


Feet. 


A 


out. 


out. 


nil. 


35 


3-96 


11-09 


B 


in. 


;i 


)) 


39i 


3-58 


8-09 


C 


out. 


in. 


. ) 


45 


5-79 


10-83 


D 


in. 


a 


1 1 


46 


518 


8-45 


E 


out. 


out. 


Homogeneous cargo 
at 51 cub. ft. per ton. 


39i 


1-68 


3-16 


F 


m. 


> ) 


ditto. 


37 


1-31 


3-12 


G 


out. 


)i 


Coal cargo at 
45 cub. ft. per ton. 


43 


2-25 


4-02 


H 


m. 


M 


ditto. 


41 


1-82 


3-92 



Condition F loaded with Homogeneous Caego. 



-1- 

Upright. 




12° Inclination. 

Deck edge 
immersed. 



37° Inclination. 

Maximum 
stability. 



79° Inclination. 

Vanishing 
point. 



Fig. 107.— Curves of Stability for a Steamer in Various 
Conditions of Ballasting and Loading. 



184 KNOW YOUR OWN SHIP. 

large angles of inclination would show ample righting arms and 
range, and the large displacement would produce large righting 
moment. To reach this enviable condition, no less than 3700 
tons of weight, including water ballast and bunker coal, would be 
required in this vessel. Ordinary double bottom and peak tanks 
provide 1000 tons towards this. The bunkers contain, say, 500 
tons of coal, and we find that 2200 tons more are wanted, which 
would require considerable provision, and entail additional outlay. 
But as shown by fig. 103, vessels of this class have such 
enormous reserve stabilijty at large angles of inclination that, in 
order to obtain a good condition of stability, it is not necessary to 
get the metacentre into the lowest position, but, as the metacentre 
lowers much more slowly as the 18 feet draught is approached, 
by arranging the ballast, the centre of gravity may be so situated 
as to give moderate metacentric height at a less draught with 
perfect safety. But we have manageableness to consider as well 
as stability, and it is probable that in order to get a satisfactory 
combination of both, the vessel should be immersed to approxi- 
mately about half the difference between light and load draught, 
which means about 2750 tons for this vessel. By way of 
illustrating positions for water ballast, examples are given in fig. 
105, though a little consideration will show that many modifica- 
tions or other combinations might be adopted. Each vessel has a 
cellular double bottom fore and aft. In all the four examples it has 
been assumed that the vessels have at least three decks, or are of 
such depth as to require three decks or an equivalent to three decks. 
Modification would naturally be necessary in vessels of less depth. 

Example 1 shows a deep tank at each end of the engine and 
boiler space. Where the fore one is shown, a cross bunker in 
many ships is located. When full of coal, the coal would naturally 
serve as ballast. By the introduction of additional strength it 
could be built to carry water as ballast when not occupied by coal. 
One or both of these tanks might better give the condition required 
by being made shorter and carried up higher. 

Example 2 shows an arrangement where one or both spaces in 
the lower 'tween decks could be constructed for ballast. 

Example 3 is another case showing the ballast higher still. In 
some vessels this method could be carried out with perfect safety, 
and a desirable metacentric height could be obtained without sacri- 
ficing, to any serious extent, the stability at considerable angles 
of inclination. A further advantage of such an arrangement of 
locating the ballast at the sides of the vessel is, that it assists in 
producing slower and easier transverse movements without making 
any draw upon the stability, such as always accompanies the 
raising of the centre of gravity. This space again could be used 



BALLASTING. 185 

for bunkers, and would naturally need special support in the form 
of strong beams, pillars, etc. 

Example 4 shows a ballast tank situated at the fore end of the 
boiler space. 

This, again, is in a common position for the cross bunker, and 
might be used for such purpose when sufl&cient coal is carried. 
Fore and after peaks, when properly constructed, may also be 
used for ballast. The disadvantage of large fore and after peak 
tanks is that, owing to the fineness of the ends of the vessel, they 
are almost unsupported, and act as hanging weights along a lever, 
causing severe straining, which is more excessive in the light con- 
dition than any other. 

In the foregoing examples the midship ballast spaces should be so 
constructed, with watertight hatches and doors, as to be thoroughly 
adapted for cargo or bunker coal, and adjusted to suit trim. 

Indeed, in designing such spaces for ballast, a foremost con- 
sideration should be to see that they are not rendered useless for 
the carriage of cargo when ballast is not necessary. Another 
important consideration is to adopt, when possible, such spaces as 
by their requirements, apart from ballast, approach nearest to the 
requirements for carrying water as ballast — such as watertight 
'tween decks, bunkers, hold spaces, etc. By this means consider- 
able saving may be made in the course of construction. 

It w^ould be absurd to propose the introduction of ballasting 
arrangements such as have been mentioned for vessels on regular 
routes, and always sure of cargo, but where there is the possibility 
and probability of occasional, and sometimes frequent, runs in 
ballast, it appears that the best sea-going conditions can only be 
arrived at by some such process. Nor could any of the methods 
illustrated be recommended before making a thorough investi- 
gation of the particular ship under consideration. 

It is true that large ballast tanks add somewhat to the cost and 
weight of a ship, though, as previously shown by the adoption of 
certain spaces, where the usual construction lends itself for such 
purpose, both cost and weight are kept down. 

However, by the reduction of overdue voyages, and less consump- 
tion of bunker coal, together with the greater safety of the vessel, 
and the often vastly improved conditions of existence for those on 
board, it would seem that additional ballast to that provided by 
the ordinary cellular double bottom, carried in tanks properly con- 
structed and adjusted, can only be worthy of commendation. 

Note. — Actually fitted water ballast tanks, showing methods of construction 
and special strengthening, are given in the author's companion volume, Con- 
struction and Maintenance of Steel Ships. 



186 , KNOW YOtJtl OWN sum 



CHAPTERVI. (Section IV.) 
LOADING— HOMOGENEOUS CARGOES. 

Contents. — Alteration to Curve of Stability owing to Change in Metacentric 
Height—Stability of Self-Trimming Vessels — Turret — Trunk. 

Loading. — All cargo-carrying vessels are not of the same type, 
proportions, or form ; therefore, they cannot all be loaded alike. 

Loading does not mean, as some would imagine, the art of 
throwing into the smallest possible hold space the greatest 
amount of cargo in the least time. This method might do all 
very well, probably, for the loading of railway trucks, when the 
freight is not of a more damageable nature than sand or rubbish, 
but to adopt such a method in dealing with so sensitive an object 
as a ship, simply betrays unwonted ignorance. Certain ships 
lend themselves more than others to the production of objection- 
able results, but in the majority of vessels built in these days, 
the person in charge of the loading or ballasting is often more 
blameworthy for the bad stability and behaviour of his ship at 
sea than the ship herself. By the term had stability is not only 
meant too short righting levers or too short range (this might 
be called deficient stability), but also too much stability, with 
too long righting arms for small angles of heel, which produces, 
as observed in Section II., rapid movements, and probably exces- 
sive rolling. 

Suppose the shipbuilder supplies a captain with a curve of 
stability for his ship in her loaded condition, with a certain 
metacentric height. This, while perfectly safe, he also finds 
produces easy motion and general steadiness at sea. As far 
as it is possible, he observes and makes notes of the distribution 
of weights in the hold, as regards their vertical and horizontal 
position — that is, if the cargo be of a miscellaneous character, and 
strives to obtain a similar condition on each succeeding voyage, 
testing at times, when doubtful, the metacentric height in the 
load condition, before sailing. Now suppose in going to a strange 
ship he proceeds to adopt exactly the same methods of loading as 
in the previous one, it is extremely unlikely that similar results 
would be obtained, for at sea we should probably find her 



LOAblitG HOMOGBNiotJS CARGOES. l8? 

behaviour widely different, and on testing the metacentric height, 
that she had either far too much, or else too little, or possibly 
scarcely any at all ; the diflference in form, proportions, type, or 
arrangement of. permanent weights being accountable for this 
result. 

Thus we see that efficient loading demands much more know- 
ledge, intelligence, and wise discretion than one would at first 
imagine. Mere rule-of-thumb methods can only produce uncer- 
tainty in the majority of cases. A clear understanding must 
exist as to what is the best condition of seaworthiness. 

For all vessels identical in their proportions, in type, and in 
internal arrangement, it would be an easy matter to fix upon a 
freeboard and metacentric height such as would ensure the best 
possible results at sea ; but the immense variety of vessels which 
are continually being built renders this impossible. However, 
the officer who superintends the loading is relieved from the 
former of these responsibilities, as this is fixed either according 
to the rules of the Board of Trade and Registration Societies, or 
else by the designers, who in some cases prefer to give more free- 
board than the rule minimum. Neither can the officer deter- 
mine the best metacentric height. Here, again, he is dependent 
upon the builders or naval architect, who, by calculation, experi- 
ment, and varied experience, are in the best position to specify 
the metacentric heights under various conditions likely to prove 
most satisfactory. The responsibility which does rest with the 
ship's officer is the obtaining of the required metacentric height, 
without which the freeboard determined by the Board of Trade 
Rules (a freeboard which is calculated on the necessary condi- 
tions being fulfilled to provide the ship in a state of seaworthiness) 
is by no means of itself a guarantee of safety. As some captains 
would remind us, it is true that probably with the majority of 
ships built no such information is provided, much less curves of 
stability. The reason has been given many times before — 
viz., that in most cases the ship's officer does not know how 
to use them if he got them. But it would be unjust to blame 
him for not understanding a subject about which so little attempt 
has been made to provide the proper means of obtaining a know- 
ledge of their meaning and use. In the past there has been even 
a worse feature than this. Probably there are no shipbuilders 
who have more endeavoured to supply information of this nature 
than Messrs William Denny <fe Brothers, Dumbarton, and yet 
their experience is the regrettable one, that only in some 
cases has their information been used. The happy side, how- 
ever, is that, when it has been used, most satisfactory results 
have been obtained. Shipbuilders have not been much en. 



188 KNOW tOUR OWN SHIP. 

couraged in the past to go to the additional trouble, except in 
special cases, of providing information upon stability. It is 
hoped, however, that with the ever - increasing facilities of 
education for persons in all occupations, the subject will no 
longer be relegated to the remote position it has hitherto held, 
especially among oflBcers of the mercantile marine. 

The writer's experience in lecturing has proved that the 
importance of all the points dealt with in this book is already 
being more fully comprehended, and that seamen generally are 
desirous of acquainting themselves with them. Undoubtedly, 
when such information can be used, shipbuilders, as a rule, will 
be only too ready to supply it, if it were for no other reason than 
the return which ships' officers would be able to make, in giving 
reliable information to the shipbuilder, which would greatly 
assist in the development of vessels thoroughly adapted for their 
special trades. 

At this stage a few observations may possibly be made with 
profit upon the loading of homogeneous cargoes. Although in 
some respects less complicated than those of a miscellaneous 
character, nevertheless their varying densities necessitate that 
their varying effects upon the vessel's stability be understood. 

Homogeneous Cargoes. — By a Jtomogeneons cargo is meant 
one all of the same kind, such as a complete cargo of cotton, or 
coal, or wool, or grain, or timber. All homogeneous cargoes 
which exactly till the holds, and bring a vessel down to her load 
waterline, have the same effect upon the levers of stability, and 
produce the same amount and range in every case. This is self- 
evident, since the centre of gravity of every such cargo must 
occupy the same position, thereby producing in each case 
identical levers of stability. As the total weight of each such 
cargo as brings the vessel to the same load waterline must be 
equal, it follows that the moment of stability, which equals the 
displacement multiplied by the righting lever, must also be 
identical ; the other conditions, metacentric height and free- 
board, which are necessary in the production of similar stability, 
remaining constant. But supposing that we have a homogeneous 
cargo of the nature of timber, which necessitates a part of it 
being placed on deck in order to sufficiently load the vessel to 
bring her down to the load waterline, then we alter the previous 
conditions, and the stability is affected. 

Having placed a part of the weight constituting the cargo 
upon the deck, it follows that the centre of gravity will have 
risen b}^ the distance of the centre of gravity of the deck cargo 
from the centre of gravity of the ship (when laden with a homo- 
geneous cargo, which simply fills the holds alone and brings her 



LOADING HOMOGENEOUS CAKGOES. 189 

down to the load waterline), multiplied by the weight of deck 
cargo, and divided by the total displacement. However, 
although the metacentre always occupies the same position 
when the vessel is at her load waterline, and the freeboard is 
constant, yet the reduction in the metacentric height, due to 
the deck timber raising the centre of gravity, will result in 
decreased levers of stability, and, consequently, decreased 
moment and range. But, again, a vessel laden with a light 
homogeneous cargo, which, like timber, does not put the vessel 
down to the load waterline when the holds are filled, and is of 
such a nature that if exposed to the weather would suffer 
damage, has, consequently, considerably more than the necessary 
freeboard. The probable result in most cases would be a 
reduced metacentric height. This would in all likelihood be 
caused by a lowering of the metacentre and raising of the 
centre of gravity. It is true that the metacentre ought, accord- 
ing to the formula, to be at a greater height above the centre of 
buoyancy, owing to the decreased displacement and very slightly 
reduced moment of inertia of the new waterplane ; but then the 
centre of buoyancy has lowered also, owing to the lesser draught, 
which, altogether, may have produced in the region of the load 
waterline a lowered metacentre (see Metacentric Curves, fig. 
115). This, however, could readily be ascertained from the 
curve of metacentres. 

Coming to the centre of gravity, we should most likely find 
that the centre of gravity of a homogeneous cargo filling the 
holds lies below the centre of gravity of the vessel in her light 
condition ; so that the loading of such cargo must produce a 
centre of gravity for the loaded ship below the centre of gravity 
in her light condition. When such is the case, it, moreover, 
follows that the heavier the homogeneous cargo, the greater its 
effect in producing the lowest centre of gravity and the greatest 
metacentric height. The lightest homogeneous cargo would 
therefore produce the highest centre of gravity and the least 
metacentric height. Thus the conclusion should not be jumped 
to that the greater freeboard will compensate for the loss of 
metacentric height and raised centre of gravity, for it might 
very possibly be found that the whole range of stability had 
suffered reduction, which would be further influenced by the 
smaller displacement. 

On the other hand, with a homogeneous cargo which puts 
the vessel down to her load waterline, and yet does not fill the 
holds, it follows that the centre of gravity must occupy a lower 
position than when laden with a homogeneous cargo filling the 
holds. The result in this case is, that the metacentric height 



190 



KNOW YOUR OWN SHIP. 



being greater and the freeboard unchanged, the lever of stability 
is lengthened and the moment and range are increased ; so that 
for a vessel engaged in general trade, the value to a shipmaster 
of a curve indicating her stability when laden with a probable 
light, homogeneous cargo, which causes her to draw considerably 
less water than her load draught, and another, when laden with a 
denser homogeneous cargo, exactly putting her down to the load 
waterline, must be obvious. 

To find Alteration to Curve of Stability owing to a 
Change in Metacentric Height. — Having given the meta- 
centric height and a curve of stability for a vessel at a certain 
draught, it is a very simple matter to find the new curve of 
stability when any change has taken place in the distribution of 




Fig. 108. 



the weights of the cargo in loading, and thereby altering the 
metacentric height, as long as the same draught is maintained. 

Fig. 108 shows a vessel floating originally at the waterline 
W L, but under inclination at the waterline W L'. B is the 
centre of buoyancy at the new waterline. G, G\ G^ are three 
positions for the centre of gravity, produced by different arrange- 
ments of miscellaneous cargo upon three successive voyages. Let 
it be assumed that a curve of stability has been provided for the 
first condition of loading. The distance from G to G^, and G^ to 
G^, is, say, 1 foot. Under the first condition of loading, the right- 
ing lever is G Z, under the second condition it is G^ Z, — that is, 
G Z reduced by the part G k, 

G A; = G G^ (1 ft.) X sine of the angle of inclination. 

G Z - (G G^ X sine of angle of inclination) = G^ Z. 

G Z - (G G^ X sine of angle of inclination) = G^ Z. 

The new levers for the curve of stability for any condition of 
loading are thus found by multiplying the distance the centre of 



LOADING HOMOGBNBOUS CARGOES. 



191 



gravity has risen by the sine of the angle of inclination, and 
deducting the result from the original levers of stability. Should 
the centre of gravity have lowered, then the correction will re- 
quire to be added to the levers of stability. (See fig. 104.) 

This is both important and exceedingly useful to a ship's 
officer. For example, his vessel's loaded seagoing draught is 
fairly constant, and having once been supplied by the designer or 
shipbuilder with the metacentric height, and a curve of stability 
for the vessel loaded with a homogeneous cargo, he can always 
readily ascertain what his curve of stability is for any other con- 
dition of loading at the same draught. This is further important, 
because the metacentric height for one vessel at the load draught 
may be quite unsuited and even dangerous for another vessel at 
her load draught. Many Atlantic liners have only a few inches 
metacentric height, being purposely designed in this way in order 
to make them easy and comfortable at sea. But there is no 
danger of their capsizing through lack of stability, for as soon as 
they begin to heel, their righting levers of stability begin to grow 



Figs. 109, 110, and 111. 



in length, owing to their great freeboard and true proportions. 
(See figs. 92, 93, 94, 106, 107.) 

In some measure this applies also to cargo vessels with 
great freeboard, such as awning and spar-decked vessels. The 
metacentric height in well-proportioned vessels of these classes, 
when properly loaded, would be satisfactory at about 1^ feet. 
Where excessive beam is adopted, it becomes almost impossible, 
and also most dangerous, to attempt to follow the metacentre in 
its high altitudes by using every possible means to raise the centre 
of gravity. There is no alternative in such vessels but to put 
up with their heavy rolling, lurching, straining, and general dis- 
comfort. 

Vessels with very low. freeboard necessarily require greater 
metacentric height, and more especially so if, in addition, they are 
very beamy. Naturally, great beam produces large metacentric 
height, unless it is overruled in the process of loading. 

Now, in designing a vessel, unless flill particulars are given of 
the exact nature of the cargo to be carried, the designer works upon 



192 KNOW YOUB OWN SHIP. 

the assumption that the holds are exactly filled by a cargo of a 
homogeneous nature. During recent years, a number of new types 
of vessels have presented themselves, such as the " Turret," 
"Trunk," and "Self-trimming" types. (Figs. 109, 110, 111.) 
There is no doubt that these vessels have certain advantages, 
especially in the nature of their self-trimming capabilities. The 
reserve buoyancy afforded by the turret, trunk, or other self- 
trimming erection is rightly taken into account in .determining 
the freeboard, and, as a result, the deck is brought much nearer 
to the water level. But with the good beam which it is usual to 
give to these vessels, ample metacentric height is provided, so 
that, when loaded with a homogeneous cargo (the only way in 
which to make a fair comparison of vessels), there is no doubt 
that their designers and builders have amply provided for all 
demands upon their stability that wind and weather are likely to 
make. 



8Hl^'J?IlJ(J CARGOElS. l93 



CHAPTER VI. (Section V.) 

SHIFTING CARGOES. 

Contents. — Variations in Stability on a Voyage. 

Shifting Cargoes. — Professor Elgar, in a most valuable and 
instructive paper read before the Institute of Naval Architects, 
in 1886, upon " Losses at Sea," states that in the three years, 
1881, 1882, and 1883, out of 264 British and Colonial vessels 
registered in the United Kingdom of and above 300 tons gross 
register, which had been lost at sea under the category of 
** foundered or missing," one-fourth of these were laden with coal, 
and one-sixth with grain — ^very large percentages of the total 
losses from these causes. It must be remembered, however, that 



A. 


c 


^^^^^^w^"^^'' 


STAR 

* 

e 

Q 


BO 

• 




jE^ 


- ~ ^^'""""'''^ 




t 


:^J^5£r>5^ 




p^ 


... _jr_ ZL**- ' / 




y — 


ffr — '" — ^"""7 





Fig. 112. — Vessel with Cargo Shifted, 

these are two of the largest trades in which British vessels are 
engaged, but at the same time it is obvious that they are two of 
the trades in which there is most possibility of cargo shifting. 
Hence the precautions insisted upon by the Board of Trade in 
the case of vessels carrying grain in bulk, that proper feeding 
arrangements be adopted in order to keep the hold spaces filled ; 
that proportions of grain to be carried in bags; and also that 
shifting boards be fitted down the centre of the holds, extending 
from keelson to deck, and in 'tween decks from deck to deck. 
Without such precautions, where both grain and coal are carried 
entirely loose in the hold, the danger is easily perceivable. 



196 KNOW YOUR OWN SHIP. 

Take an ordinary cargo vessel which on a six days' voyage 
from one port to another consumes, say, 100 tons of . coal. 
Naturally the displacement will be reduced by 100 tons, and 
by referring to the " tons per inch " curve it may be ascertained 
how many inches the draught has decreased, evidently giving 
greater freeboard in the first place. 

The effect upon the metacentric stability will depend chiefly 
upon the position of the centre of gravity of the bunker coaL 
In the case where the bunkers are situated on each side of the 
boilers, and in a cross bunker extending from the top of the 
floors to the first deck when there are two or more decks, the 
centre of gravity of the bunker coal will generally lie below the 
centre of gravity of the ship, making the ship stiffer. When 
the coal is consumed the vessel will become more tender, and 
usually steadier when among waves, due to the reduced meta- 
centric height. 

But as is more common in these days among tramp steamers 
of good beam, where, in order to get the greatest reduction on 
the tonnage by obtaining the largest possible propelling space 
(see Tonnage), the practice of almost dispensing with lower side 
and cross bunkers is adopted, and the coal is carried in the 
'tween decks at the sides of the engine and boiler casings. 
Frequently an additional 30 or 40 tons are placed on the bridge 
deck, and kept there by means of temporary boards secured to 
the rails, or by closed-iron bulwarks. In such cases the centre 
of gravity of the coal is much above the centre of gravity of the 
ship, producing reduced metacentric height and greater steadi- 
ness. But on the consumption of this coal, the top weight 
being removed, the centre of gravity lowers, the ship becomes 
stiffer, and is found to roll more than previously. 

After lecturing on this subject on a certain occasion recently, 
a captain who was one of the audience related the following 
uncommon incident in his own experience, an incident which he 
had never been able to understand : — 

Coming up the Irish Sea to Liverpool almost at the end of a 
homeward voyage, laden both in holds and on deck with esparto 
grass, the vessel began to indulge in most peculiar movements. 
There was not much sea, and previous to this time the vessel 
had been exceedingly steady ; but now she commenced to take 
a slight list, and to move occasionally from side to side with a 
jerk, and not with a rolling motion. She would then lie still 
after one of these movements, except for the rising and falling 
of the waves, until after another interval another wave lifted 
her up, and she jerked to the other side, there again lying for a 
time, the motion being repeated at intervals. As this captain 



SHIFTING GARQOBS. 



195 



the hold is at as large an angle a^ the surface of the heaped 
grain, before any shilt takes place. If the ship could be heeled 
Blowly and steadily, no shift of cargo would occur before the 
surface of the grain has reached aa great an angle as it is possible 
to heap it upon a floor, as in fig. 113, ab and a & being at the 
same angle of inclination. 

If this answer were correct in all cases, possibly a littls less 
uneasiness might be felt as regards shifting cargo, for the late 
Professor Jenkins, in a paper read before the Institute of Naval 
Architects, on this subject, gives the ■greatest angles to which 
it is possible to heap a free surface of wheat (or, as it is termed, 
the angle of repose) at 23J°, which is considerably less than that 
of most grain, and as grain-laden vessels are generally inclined 
to be tender, and, therefore, usually roll less, the angles of repose 




Fio, 113.— Ahqle of Repose poa Graih. 

for grain are greater than many such vessels would roll through. 
But this is not the case, for the effect of rolling, pitching, and 
blows from the sea is to reduce the angle of repose considerably. 
Moreover, movement of cargo will take place aU the sooner, the 
gi-oater the distance its surface is situated from the centre about 
which the ship rolls ; hence, cargo in the 'tween decks will shift 
sooner than cai^o in the hold. 

"When it is known that shifting boards extending down the 
middle line of a ship reduce the heeling moment of shifted cargo 
to about one-fourth of what it would be without them, their 
value will then bo better understood. 

Variationa in Stability on a Voyage. — Steamers are 
especiaUy liable to considerable change in their stability and 
behaviour at sea between the time of leaving one port and 
arriving at another. 

This is chiefly due to 'the consumption of bunker coal. 



196 KNOW YOUR OWN SHIP. 

Take an ordinary cargo vessel which on a six days' voyage 
from one port to another consumes, say, 100 tons of . coal. 
Naturally the displacement will be reduced by 100 tons, and 
by referring to the " tons per inch " curve it may be ascertained 
how many inches the draught has decreased, evidently giving 
greater freeboard in the first place. 

The effect upon the metacentric stability will depend chiefly 
upon the position of the centre of gravity of the bunker coal. 
In the case where the bunkers are situated on each side of the 
boilers, and in a cross bunker extending from the top of the 
floors to the first deck when there are two or more decks, the 
centre of gravity of the bunker coal will generally lie below the 
centre of gravity of the ship, making the ship stiffer. When 
the coal is consumed the vessel will become more tender, and 
usually steadier when among waves, due to the reduced meta- 
centric height. 

But as is more common in these days among tramp steamers 
of good beam, where, in order to get the greatest reduction on 
the tonnage by obtaining the largest possible propelling space 
(see Tonnage), the practice of almost dispensing with lower side 
and cross bunkers is adopted, and the coal is carried in the 
'tween decks at the sides of the engine and boiler casings. 
Frequently an additional 30 or 40 tons are placed on the bridge 
deck, and kept there by means of temporary boards secured to 
the rails, or by closed-iron bulwarks. In such cases the centre 
of gravity of the coal is much above the centre of gravity of the 
ship, producing reduced metacentric height and greater steadi- 
ness. But on the consumption of this coal, the top weight 
being removed, the centre of gravity lowers, the ship becomes 
stiffer, and is found to roll more than previously. 

After lecturing on this subject on a certain occasion recently, 
a captain who was one of the audience related the following 
uncommon incident in his own experience, an incident which he 
had never been able to understand : — 

Coming up the Irish Sea to Liverpool almost at the end of a 
homeward voyage, laden both in holds and on deck with esparto 
grass, the vessel began to indulge in most peculiar movements. 
There was not much sea, and previous to this time the vessel 
had been exceedingly steady ; but now she commenced to take 
a slight list, and to move occasionally from side to side with a 
jerk, and not with a rolling motion. She would then lie still 
after one of these movements, except for the rising and falling 
of the waves, until after another interval another wave lifted 
her up, and she jerked to the other side, there again lying for a 
time, the motion being repeated at intervals. As this captain 



SHIFTING CABG0B8. 197 

now explained, the vessel having a light homogeneous cargo, 
had been very tender, and all the more so with the deck cargo. 
The bunkers being situated low down in the vessel, the con- 
sumption of coal on the homeward voyage must undoubtedly 
have still further reduced the metacentric height. Moreover, 
during the latter part of the voyage the deck cargo became 
soaked with rain, which made it heavier and more effective in 
raising the centre of gravity, until at last the centre of gravity 
actually coincided with or rose above the metacentre. In the 
latter case an upsetting lever having arisen, the vessel heeled, 
until by the immersion of a new wedge of buoyancy this heel- 
ing force was absorbed. The vessel was now practically in a 
similar condition to the homogeneous cylinder we considered in 
tig. 98, except that on being still more inclined, the immersion 
of another new wedge of buoyancy caused the righting levers of 
stability to grow again, which resisted further inclination. 

Thus the cause of the vessel jerking from side to side was not 
due to the effect of any righting moment, but simply to the 
heaving motion of the sea pushing her occasionally to the up- 
right, and then losing her balance, being in a state of neutral 
equilibrium, she dropped over to the other side. 

Any vertical movement of weights, or increase or decrease of 
weights already on board, will in some degree influence the 
stability, which, as has been shown, will affect her motion among 
the waves. 

Emptying or filling water ballast tanks may have a similar 
effect. 



198 



KNOW TOUR OWN SHIP. 



CHAPTER VI. (Section VI.) 

BPPBCT OP ADMISSION OP WATER INTO THE 

INTERIOR OP A SHIP. 

Contents. — Admission through a hole in the Skin into a Large Hold — 
Curves, showing Variation in Height of Metacentre with Increase of 
Draught — Buoyancy afforded by Cargo in Damaged Compartment — 
Longitudinal Bulkheads — Entry of Water into Damaged Compartment 
beneath a Watertight Flat— Entry of Water into Damaged Compart- 
ment above a Watertight Flat — Value of Water Ports — Water on 
Deck — Entrance of Water through a Deck Opening — Entry of Water 
into an End Compartment — Height of Bulkheads — Waterlogged 
Vessels. 

Effect of the Admission of Water into the Interior of a 
Ship. — 1. Through a hole in the Skin below the Load Water- 
line : — 

Let fig. 114 be a box-shaped vessel 100 feet long, 20 feet broad, 
10 feet draught, and 5 feet freeboard. For the saJke of example. 



-w 








i. 


~yN 




fiS^ 




?* 














i¥s^3 


• 








f = £^s 







Fig. 114. — ^Effect of Entry of Water into a Central 

Watertight Compartment. 

let there be a watertight compartment, one-fourth of the length 
of the vessel — viz., 25 feet -—situated at the middle of the length, 
and bounded at each end by a watertight bulkhead, as shown. 
We will suppose this compartment to be damaged by collision, 
and the sea to enter by the hole indicated. 

After the damage the draught of water will have increased 
from W L to wl^ for, as was pointed out in the Chapter on 
Buoyancy^ the buoyancy of the compartment into which the 
water has entered having been lost, in order to support the 
weight of the vessel which remains unchanged, the reserve 
buoyancy in the other intact compartments has had to be drawn 
upon, hence the increase of draught. But let us see what effect 



EFFECT OF ADMISSION OF WATER INTO SHIFTS INTERIOR. 199 

this has had upon the metacentric height. The rule for the 
height of metacentre above centre of buoyancy is — 

Moment of inertia of waterplane 
Displacement in cubic feet 

Now, in taking the moment of inertia of the new waterplane of 
this vessel, the compartment into which the sea has entered is 
entirely ignored, and treated as though it were no part of the 
vessel, since it affords no buoyancy. The moment of inertia of 
the new waterplane w Z, less the part F G, divided by the dis- 
placement, gives the height of the metacentre above the centre of 
buoyancy. It will be pretty evident that the moment of inertia 
will have decreased considerably owing to the loss of a part of the 
waterplane area, which must result in bringing the metacentre 
nearer to the centre of buoyancy. The position of the centre of 
gravity of the ship remaining unchanged, it would appear to 
follow, at first sight, that in every such case the metacentric 
height is reduced. But let not the important fact be overlooked 
that the centre of buoyancy must have risen with the increase of 
draught. Possibly a simple calculation may more effectively 
throw further light upon this. Referring to the box vessel before 
the accident occurred : — 

The displacement was 100 x 20 x 10 = 20,000 cubic feet. 

The moment of inertia of the waterplane = ^ ^ - 66666. 

*^ 12 

The metacentre above centre of buoyancy = — ~ = 3*3 feet. 

^ ^ 20000 

The metacentre above the bottom of the box is 5 + 3*3 = 8*3 feet. 

Let the centre of gravity be, say, 6*3 feet from the bottom of the box, 
then the metacentric height in the undamaged condition is 8*3 - 6*3 = 2 feet. 

For curve of stability (see fig. 87, curve No. 3). 

After the collision, the draught is found to have increased 3*3 feet; this 
is arrived at by dividing the volume of the lost buoyancy F G B A (fig. 114) 
by the total area of the waterplane, less the part F G. 

The centre of buoyancy is therefore — 

^^ '*' ^'^ = 6*6 feet from the bottom of the box. 
2 

The displacement remains unaltered at 20,000 cubic feet. 

75 X 20^ 
The moment of inertia of the waterplane = - — = 50000. 

*^ 12 

The metacentre above the centre of buoyancy = = 2*5 feet, 

^ ^ 20000 

which is lower than formerly. 

The metacentre above the bottom of the box = 6*6 + 2*5 = 9*1 feet, 
which is higher than formerly. 

Then the metacentric height after the collision is 9*1 - 6*3 = 2*8 feet, 
which is greater than formerly. 



200 KNOW YOUR OWN SHIP. 

Thus we see that the vessel has actually a greater metacentrio 
height after the accident with the compartment flooded than she 
had originally in her intact condition. At first, one is almost 
tempted to jump to the conclusion that this could scarcely be 
the result, for if such be the case, why the loss of so many 
vessels subdivided into numerous watertight compartments ? and 
we may point to the battleship " Victoria," and the more recent 
disaster to the "Elbe." To understand this, it is necessary to 
carefully trace the effect of the chief influencing agents, upon 
which the initial or metacentric stability depends, from the 
moment the collision happens to its climax. Be it observed, 
however, that while the metacentric stability is less for this 
box ship in the undamaged condition, yet the stability for 
greater angles of inclination is unquestionably superior. This 
is accounted for by the greater freeboard. Moreover, all ships 
cannot bo classed as boxes, and the difference in form and the 
fining away of the waterlines (or beams) towards the ends, has a 
very marked efl'ect upon the height of the metacentre, owing to 
the great reduction in the moment of inertia of the waterlines. 

Variation in Height of Transverse MetSrCentre owing to 
Increase of Draught. — It is generally found in merchant 
vessels that for light draughts the metacentre is highest, owing 
to the small displacement in comparison with the moment of 
inertia of the waterlines, but as the draughts increase the 
immense bulk of the vessel grows more rapidly in proportion 
than does the moment of inertia. The result often is that the 
metacentre falls, until, when approaching the load waterline, the 
lowering effect of the increasing displacement is less than the 
raising effect of the centre of buoyancy, owing to the increasing 
draught, and the metacentre rises again.* This leads us to the 
important fact that dangerous as the shipping of heavy seas 
may be into large wells upon the decks of many vessels, yet in 
some cases, owing to the increased draught from such sudden 
deck weight the metacentre rises, and this greatly tends to 
avert what might often be a serious condition. 

In fig. 115 several examples are given for different types of 
actual ships, showing the effect of increased draught upon the 
heiglit of the metacentre, as shown by the curves. The table 
on the same page gives the particulars for each vessel. 

It will also be noticed that a collision happening in way of a 
moderately large compartment at or near amidships, the loss of 
this most effective moment of inertia of waterplane (the beam 
being greatest here), greatly modifies the results obtained from 

* Flaro out on the load watorlino at the ends of a vessel increaBOS thQ 
ni^oxDent of inertia and tends to produce the 8ai;ne results, 



EFFECT OF ADMISSION OF WATER INTO SHIp's INTERIOR, 201 

vessels of box form, and makes impossible such increase in meta- 
centric height as is obtained from our box vessel with its central 
compartment flooded (fig. 114). In the box vessel in our illus- 



2^ 



zz ' 



2.0 



a> 



<u 




M 


JS - 


«m 




o 




% 


16 ' 


H 




«i 




> 




o 


M- 


J=> 




a 




*a 




4) 


72- 


««H 




a 




•^^ 




CO 

4J 


70' 


fii 




«fi 








a> 




A 


9 ■ 


••-. 




o 




(i> 





« 



c • 



z • 




of Draughts in feet. 



Fio. 115.— Curves of Metacentres, showing Upward Tendency 

IN Region of Load Draught. 



No. of 

Vessel. 

1 


Leugth. 


Breadth. 


Depth 
Moulded. 


Load. 
Draught. 


Description. 




Feet. 


Ft in. 


Ft. in. 


Ft. in. 




1 


320 


45 3 


28 


22 


Full sailing ship. 


2 


270 


41 


26 3 


21 


Full sailing ship. 


3 


206 


28 6 


15 10 


14 


Fine steamer. 


4 


231 


32 


17 4 


15 


Moderately full steamer. 


5 


215 


31 10 


16 3 


15 


Moderately full steamer. 


6 


245 


33 


17 3 


15 9 


Moderately full steamer. 


/ 


190 


27 6 


18 


12 


Steam yacht. 


8 


162 


22 


14 4 


11 6 


Steam yacht. 


9 


154 


22 


13 6 


9 


Steam yacht. 



202 



KNOW YOUR OWN SHIP. 



tration the draught was 10 feet, and the freeboard 5 feet, and if 
these figures be for loaded conditions, the amount of freeboard, 
and, consequently, reserve buoyancy, is exceptionally great. 

Had there been anything less than 3*3 feet freeboard she would 
have foundered, the weight of the vessel more than swamping the 
total remaining buoyancy after the collision. But probably neither 
the ** Victoria " nor the " Elbe " sank from this cause, for before 
the reserve buoyancy had been exhausted they capsized. 

Let fig. 116 represent the section of a vessel in way of a 




Fig. 116.— Influx of Water into Damaged Compartment. 

damaged compartment, the buoyancy of which compartment is 
less than the remaining reserve buoyancy, thus proving that 
there is, at any rate, capacity to float after the inflow of water 
has ceased. 

Water flows in through the hole X, and if the hole be large, 




Fig. 117. — List Caused by Influx of Water. 

as it usually is under such circumstances, the immense weight 
of water which rushes in on tJie one side^ together with the 
natural tendency of water to find the lowest possible positioDp 
has the effect, for the time being, of drawing out the centre of 
gravity of the vessel in the same direction — that is, towa|r4B tb© 



EFFECT OF ADMISSION OF WATER INTO SHIP's INTERIOR. 203 

side of the ship where the hole is, and the vessel takes a list. 
The water already in the compartment naturally seeks a hori- 
zontal surface, as shown in fig. 117, with its centre of gravity g, 
well over to the heeling side, adding to the inclination. 

The continuous pouring in of water, accompanied by increasing 
list, and the added effect of the water which has already entered, 
combine to increase the heeling process, and thus eventually, in 
many cases, when the heeling moment from these causes exceeds 
the greatest righting moment indicated by the vessel's curve of 
stability, she capsizes. If the vessel be very stiflf in the upright 
condition, in some cases she will resist the heeling caused by the 
water pouring in, and she will do this all the more easily after 
a moderate quantity has entered, as this has the effect of lowering 
the centre of gravity and adding to the stiffness and resistance 
to further inclination, and eventually, when the reserve buoyancy 
has been drawn upon for the loss of the buoyancy of the damaged 
compartment, she may remain at rest in a condition of stable 
equilibrium, unless the change of trim has been so great as to 
cause the vessel to go down by the head or the stern 

Buoyancy afforded by Cajrgo. — It should be noted that 
immediately after the collision the weight of water pouring in 




c o 

Fig. 118. — Effect of Water in a Compartment with Cargo. 



acts exactly as deadweight, lowering the centre of gravity and 
increasing the draught. But after the compartment is filled to 
the level of the water outside the ship — and the water inside the 
ship continues to be freely in contact with the water outside — 
the entered water is no longer considered as weight, any more 
than the water outside the ship is weight, since this space has 
ceased to represent floating power (excepting the cubic capacity 
of the cargo inside, if there be any, for displacement is always 
actual buoyancy), and the entered water is, therefore, dismissed 
as being no part of the vessel ; in fact, the vessel is now identical 
with fig. 118. 

Here we have two intact end compartments. The middle 
space, A B C D, has only, say, a bottom upon which rests weights 
representing cargo. There are no sides to this compartment, but 
simply the means for holding the structure together. In this 



204 KNOW TOUR OWN SHIP. 

example we have an exact illustration of the vessel we have been 
considering. The whole is being supported by the buoyancy of 
two intact end compartments, together with the volume of the 
cargo, which also affords its cubic capacity of buoyancy, though 
beneath the water level. The centre of gravity is the actual 
centre of the weight of the ship and her cargo, the water in the 
space over the cargo neither affecting its position nor adding to 
the weight. 

Thus we see that in an actual ship the entry of water may at 
first affect the centre of gravitj'', yet after the inflow has ceased, 
having reached the water level outside, the centre of gravity is 
again in its original position. If the vessel is tender in the 
upright condition, she will heel all the more easily under the 
effect of water so entering. 

Longitudinal Bulkheads. — Should the vessel possess a longi- 
tudinal watertight bulkhead down the middle of her length, 
instead of this providing a means of safety, as is sometimes sup- 
posed in such an accident, it simply adds to the effect of the 
water in heeling the ship, and by robbing the ship of buoyancy 
upon one side only tends all the more to the proiiuction of the 
often disastrous result. In cases of war and passenger vessels, 
where a system of exceedingly numerous watertight compart- 
ments is adopted, damage to one or more of these compartments 
may not produce very serious results, though possibly causing a 
list owing to loss of buoyancy, perhaps, on one side only. Being 
devoid of this floating support, the centre of buoyancy can no 
longer lie in the middle line of the vessel, but in the centre of 
the actual remaining immersed buoyancy, though, if the vessel 
remain at rest, it follows that the centre of gravity and the centre 
of buoyancy are in the same vertical line. 

It should be observed, however, that the loss of many vessels, 
thoroughly subdivided into watertight compartments, is often 
due to the fact that they have so many watertight but unclosed 
doors. Collisions generally happen at unexpected moments, and 
often in fine weather, when many of these doors are open, with 
the result that when the collision occurs, they cannot be reached, 
or are entirely forgotten, and hence the result. 

Entry of Water into a Compartment beneath a Water- 
tight Plat. — Instead of the whole middle compartment being 
open to the inroad of the sea after damage to the skin, let us 
suppose that a watertight flat or partial deck situated at one- 
half the depth of the original draught (5 feet) be fitted as in 
fig. 119, and the sea to enter through a hole into the lower com- 
partment. Let us now observe the effect upon the metacentric 
height. The waterline being entirely intact, the moment of inertia 



EFFECT OF ADMISSION OF WATER INTO SHIP*8 INTERIOR. 205 

must be reckoned upon the whole area. The metacentre is 3*3 
feet above the centre of buoyancy as for the vessel undamaged. 



-* ^— — — — — — — — — — ^-— .^— — — — ^.^— — — .. 



Fig. 119. — Effect of Entry into a Watertight Compartment 

BELOW Partial Deck. 

The volume of the lost buoyancy of the compartment B, divided by 
the area of the effective waterplane, gives the increase of draught — 

2500 



2000 



= 1 '25 feet = increase of draught. 



The centre of buoyancy of the intact end compartments only, 
from the bottom, is — 

i^jti:?? = 5-62 feet. 
2 

The effect of the buoyancy above the watertight flat is to raise 
the centre of buoyancy for the whole vessel to 6*01 feet above 
the bottom. 

The metacentre above the centre of buoyancy is 3*33 feet. 

The metacentre above the bottom of compartment is 6*01 + 3*33 
= 9-34 feet. 

The centre of gravity above bottom of compartment is 6*3 feet. 

Therefore, the metacentric height is 9*34 - 6*3 = 3 feet, which 
is greater than for the vessel in the original intact condition, 
and also, as in the foregoing example, where the whole com- 
partment between the watertight bulkheads is lost buoyancy. 
Moreover, with intact waterline and upper buoyancy, a little 
study of the wedges of immersion and emersion will abundantly 
prove that in every respect its stability is improved. 

Entry ofWater into an Upper Compartment. — But again, 
supposing the upper compartment to have been damaged, as in 



f^^ 



Fig. 120.— Effect of Entry of Water into an Upper Compartment. 

fig. 120, we shall see that the effect is greatly different. First 
of all, the moment of inertia is reduced owing to the loss of the 



206 KNOW YOUR OWN SHIP. 

space F G. The moment of inertia of the waterplane, and, conse- 
quently, the height of the metacentre above the centre of buoy- 
ancy, are now the same as in fig. 114, the latter being 2*5 feet. 
The loss of buoyancy below the waterline is the same as in the 
last case, but the increase of draught is more, owing to the 
effective area of the waterplane being reduced by the space F G. 

The increase of draught is — ^ = 1'66 feet. 

'^ 1500 

The centre of buoyancy of the intact end compartments only 
above bottom of box is — 

lO+i:?? = 5-83 feet. 
2 

The effect of the buoyancy below the watertight flat is to lower 
the centre of buoyancy for the whole vessel to 5*42 feet above the 
bottom. 

The metacentre above centre of buoyancy is 2*5 feet. 

The metacentre above the bottom of the box is 5*42 + 2*5 = 7*92 
feet. 

The centre of gravity above the bottom of the box is 6*3 feet. 

Therefore, the metacentric height is 7*92 - 6*3 = 1*6 feet. 

It will be very clear that this case is vastly different from the 
previous one, for not only are the metacentric height and free- 
board less, but the total loss of the upper buoyancy above the 
watertight flat will greatly reduce the effect of the immersed 
wedges in producing the levers of stability. 

Value of Water Ports. — Effect of water on deck, and necessity 
of ample freeing ports. 

In well deck vessels of the raised quarter deck type, and also 
those with poop, bridge, and forecastle, special care should be 
taken that ample means be provided for speedily ridding the 
space between the forecastle and the bridge, and also between 
the bridge and the poop, of water accumulated through tte 
shipping of heavy seas. In addition to the discomfort and the 
strain to the structure from such sudden and heavy deck weights, 
the vessel's stability may, under certain circumstances, be seriously 
affected, and if the water be not rapidly cleared, may prove a 
source of real danger. This is easily perceived when we con- 
sider the enormous weight which from time to time is poured 
on the deck during heavy weather, and this weight being con- 
siderably above the centre of gravity of the ship, the effect is 
to raise the centre of gravity possibly as high as the meta- 
centre. 

Suppose a vessel of 2000 tons load displacement has a well 
between the bridge and the forecastle 60 feet long, 34 feet 



EJ'FflCT? OF ADMISSION Of WAI'EIR iNl'O SHIP S INl^BRIOR. S07 

broad, and with bulwarks 4 feet high. This space would hold 

60 X 34 X 4 

— = 233 tofts. That shipped seas would often entirely 

fill this space would be unlikely ; but suppose, for example, 
that it be three-fourths filled, the water shipped would w^eigh 
175 tons. The centre of gravity of the weight being, say, 10 
feet above the centre of gravity of the vessel, the effect is to raise 

the position of the latter — -— — — = 0*8 of a foot. 

^ 2000 + 175 

Supposing the vesseFs metacentric height to be '6 of a foot — not 
at all uncommon in many cases of loading — then the centre of 
gravity is now approximately 0*2 of a foot above the metacentre, 
supposing no rise to have occurred in the height of the latter. 
In this condition it follows that the vessel is unable to remain 
upright, apart from the influence of the waves, and commences 
to heel, the water all rushing towards the inclining side. The 
original metacentric height is only regained by the water pouring 
over the bulwarks and through the freeing ports, which latter 
should therefore be amply sufficient to speedily clear the deck. 

The danger will be all the more obvious in vessels possessing 
deep wells, the bulwarks of which extend to the height of the 
bridge and forecastle, usually about 7 feet. It will be evident 
that such a vessel, unless capable of speedily relieving herself of 
the water through the water ports, will heel to a greater angle 
before getting rid of much of it over the bulwarks. The con- 
centration of this water to one side, when inclined, and the 
possible synchronism of a wave, may lead to disastrous results. 
Certainly, as some reader may suggest, this is an extreme case, 
but the fact that so many vessels are, in ignorance, sent to sea 
unsea worthy, and so many are recorded annually as "foundered," 
and "unheard of," demands attention, and furthermore proves 
that extreme cases are not so uncommon as is often imagined. 

Entrance ofWater through a Deck Opening. — Effect upon 
Stability owing to the Admission of Water into tJie Interior, either 
through a Damaged Deck or Deck Opening. — This case differs 
from the previous ones in the fact, that the skin being perfectly 
intact, there is no free communication between the water inside 
and outside of the vessel. There is, therefore, no loss of buoy- 
ancy, the entered water acting directly as deadweight, and 
thereby increasing the draught. If this operation were to con- 
tinue until the total weight of displacement exceeded the total 
buoyancy, the vessel would sink. Should the entered water be 
only moderate in quantity, through, perhaps, leakage in the deck 
during heavy weather, let us briefly . observe the possible effect 
upon the stability. 



208 



liNOW tOUft OWK Sfll^. 



If the vessel be very flat on the bottom, the effect, as Professoi? 
Elgar very aptly points out in the paper previously referred to, 
will be similar to that of water poured slowly into a box. Water 
naturally seeks the lowest position, and this will only be accom- 
plished by the vessel inclining, and lowering one of the bottom 
comers. At first, only a slight list is perceived, but as the 
amount of water in the interior increases, the list continues to 
increase until the centre of gravity of the water finds a position 
in the vertical line through the centre of buoyancy, after which, 
the water, which was previously the inclining element, now 
resists further inclination. 

Let fig. 121 be a vessel which has gone through these stages of 
inclination. If she then remains at rest it proves at once that 
the vertical lines through the centre of gravity and the centre 
of buoyancy coincide, the centre of gravity having moved from 




Fig. 121. — Effect of Water Collected in the Bottom of a Vessel. 



G to G', owing to the effect of the shifted water. If a vessel 
has more righting moment of stability (righting lever x displace- 
ment) at any angle of heel than the inclining moment at corre- 
sponding angles (weight of water x perpendicular distance 
between g g)* then the vessel will return to the upright. The 
vessel in our example (fig. 121) was more tender, for as the 
water entered slowly she inclined gradually, thus showing that 
the heeling moment of the water was exactly absorbing the 
righting moment of the vessel, and thus leaving her, at each 
successive angle of inclination, in a state of neutral equilibrium. 
She could not heel all at once to her greatest angle of inclination, 
simply because the heeling moment was not sufficient to absorb 
the righting moment of the vessel until more water had entered. 
In fig. 121 let the weight of water in the hold be 50 tons, and 

* ^ is centre of gravity of water in upright condition, and ff in inclined 
conditioD. 



BPPBCT OP ADMISSION OP WATER INTO SHIP's INTERIOR. 209 

the displacement of the vessel in this condition 1000 tons. In 
the upright condition the centre of gravity of the water was at 
g^ but after the inclination it is found to have travelled 6 feet, 
to g'. The effect is to draw out the centre of gravity of the 
vessel in the direction of the moved water, which distance is 
50 x6 n o c I* J. 

-j^^=0-3ofafoot. 

Owing to the shift of the centre of gravity a distance of 0*3 of a 
foot, to, say, starboard side, the effect is the same as deducting 
0*3 of a foot from the lever of stability with no water in ; and thus 
where the curve of stability shows 0*3 of a foot of lever, there would 
in reality be no lever at all, and at this angle the vessel would 
lie at rest if undisturbed. If the vessel were forcibly inclined 
further, she would probably return to this position again imme- 
diately on the inclining force being removed, proving that 
beyond this angle her righting moment exceeded the heeling 
moment of the water. 

If the vessel were now forcibly heeled to the port side and 
again left undisturbed, she would lie at the same angle of 
inclination as on the starboard side. Should it happen that the 
greatest righting lever of the vessel at any angle of inclination 
did not exceed 0*3 foot, she would undoubtedly capsize. 

The more rise there is on the bottom of the vessel, the less 
danger or likelihood is there of water thus taking a permanent 
shift, since this form of bottom makes the upright the lowest 
position that entered water can find. In such a case, the entry 
of a moderate quantity of water is to lower the centre of gravity 
and give more metacentric height. But at the same time it will 
be remembered that great metacentric height conduces to heavy 
rolling, which motion will be transmitted to the water inside, 
tending, it is possible, to incline the vessel further than she 
otherwise would. These latter remarks apply also to free water 
in partially filled water ballast tanks, and show why vessels 
which are very tender when light — which tenderness is some- 
times further augmented in the operation of coaling — so easily 
incline and sometimes take a sudden lurch. This generally 
happens at the unexpected moment, so that, as in the case 
of the " Orotava," which capsized in Tilbury Dock in December 
1896, coaling ports, or side scuttles, or other openings are sud- 
denly brought below the water surface, capsizing ultimately 
ensuing. 

Entry of Water into an End Compartment. — ^Thus far it 
will be observed that only the effect upon transverse motion has 
been dealt with, and that in the foregoing examples the water is 
supposed to have entered into a compartment in the middle of 

o 



210 



KNOW YOUB OWN SHIP. 



the length, and thus to have increased the draught uniformly 
all fore and aft. However, where a compartment is damaged at 
or near the ends of the vessel, not only may there be tendency 
to transverse inclination, but longitudinal also. 

Thus in fig. 122 let G bo the centre of gravity and B the 
centre of buoyancy in the intact condition. Should the vessel 
be now damaged through collision in the fore compartment, 
C D, and the sea find free entrance, then the buoyancy of this 
compartment being lost, the draught must increase, and the 
centre of buoyancy will endeavour to shift into the centre of 



ftf It 



I 



^— «» « ^ *^<v • 



Fio. 122,— Effect of Entry of Water in Fore Compartment. 

the remaining buoyancy, B'. But the centre of gravity and the 
centre of buoyancy being no longer in the same vertical line, a 
condition of unrest is the result, there being a lever set up 
between the vertical lines through these two forces. The vessel 
will, therefore, heel longitudinally and go down by the head, and 
will not come to rest till the centre of buoyancy is again in the 
same vertical line with the centre of gravity. The larger the 
compartment damaged, and the greater its distance from the 
original centre of buoyancy, the greater will be the change of 
draught and trim, with, possibly, disastrous results, for it will 
be seen that immediately the stem has gone under water, when 
such calamities happen there are possibly several deck openings 
or comj)anions uncovered, and the sea finding inroad through 
these, adds to the effect by making its way to that end of the 
vessel which is inclined. 

Height of Bulkheads. — It will now be better understood 
why a watertight bulkhead should be placed at a short distance 
from each end of all vessels, for these localities are most likely 
to suffer in case of collision, and, moreover, being at so great 
a distance from the centre of buoyancy, their loss of floating 
moment is great. Hence the necessity of carrying all bulk- 
heads, and especially watertight ones, as high as possible, in 
order to prevent water finding its way over the tops of them 
into the next c()ni])artments. 

Waterlogged Vessels.— It is not ixxi uufrecjueut sight during 



BPPBCT OF ADMISSION OF WATER INTO SHIP's INTERIOR. 211 

bad weather in the Baltic, where such a large percentage of the 
export trade is in timber, to see an old wooden ship, laden with 
timber in both holds and on deck, in a waterlogged condition. 
There she lies with a heavy list, rising and falling with each 
successive wave, with scarcely ever a movement of her own 
(fig. 123). 

She has sprung a leak, and water has found its way into her 
hold and risen to the level of the sea outside. There being now 
free communication between the sea and the water inside, the 
whole of the interior space unoccupied by timber — every crevice 




Fig. 123.— Waterlogged Timber-ladbn Vessel. 

and corner — is lost buoyancy. The result is the draught in- 
creases, but not the displacement, until a volume of water has 
been displaced by the timber and the framework of the vessel 
equivalent to the original volume of displacement. Undoubtedly 
the centre of buoyancy has risen. It will now be situated in the 
new centre of displacement, which no longer constitutes the 
portion of the ship which is immersed and within the skin, but 
the centre of the immersed portion of ship and timber unoccu- 
pied by water. The centre of gravity has remained stationary. 
If the metacentre had remained in the same position relatively 
to the centre of buoyancy, the ship, since the centre of buoyancy 
has risen, would actually be stiffer than before the leak took 
place, when she was probably very tender. The permanent list 
proves that such is not the case, and we can rightly come to the 
conclusion that a considerable reduction has occurred in the 
height of the metacentre. 

It has not been caused by the displacement, for that is un- 
changed. It can only lie in the moment of inertia of the new 
waterline, which is no longer for the whole area of the waterplane 
at which the vessel floats, but simply for the sectional area of 
actual timber (both cargo and ship) at that waterline. It will 



212 KNOW YOUR OWN SHIP, 

now be found that the moment of inertia is considerably leaA, 
and when divided by the displacement, gives a position for the 
metacentre below the centre of gravity. The vessel is, therefore, 
unstable, and heels over, and possibly iu some cases, were it not 
for the volume of wood on deck, she might capsize altogether. 
But she is prevented from this by the effect of the immersed 
wedge of timber, which acts as freeboard, giving buoyancy 
exactly where it is most needed to keep the vessel afloat. 

The effect has been to draw out the centre of buoyancy from 
the original position B to B', fig. 123, until the vertical line 
through the new centre of buoyancy coincides with the vertical 
line through the centre of gravity. The vessel now rests in a 
state of neutral equilibrium, having no righting lever of stability 
at this angle of inclination. 



HAILINQ, SAIL AttHA, BUc!. 



CHAPTEtl VI. (SBcriOti Vll.) 

SAILING, SAIL ABBA, etc. 

Sail Area. — In briefly considering the subject of the capability 
of a vessel for carrying sail, our study of " Momenta," Chapter II., 
again proves of great assistance ; moreover, we shall also discover 
that sail area is inseparably connected with stability. 




fiQ. 124.— TEBKH-UAsTKn SoBOONEa-RiooKS Vbssbl. 



Fig. 124 is an outline sketch of a three-masted schooner-rigged 
vessel, which will serve as an example for reference. 

Sails might aptly be compared to a number of weights ranged 
miscellaneously along a lever ; the lever would, therefore, be an 
imaginary line passing from the region of the hull to beyond the 
topmast sails. Before we could possibly calculate the moment of 
pressures about a point at the end of a lever, we should have to 
determine the position of the end of the lever from which the 
moments are calculated. Exactly the same thing takes place in 
dealing with sails ; we must determine the end of the imaginary 
lever. This point is called the csiiire qf lateral reeUiance, and 
is the centre of the resistance of the water to lateral or broadside 
motion. Such movnment would, therefore, be square, or at right 



^4 KNOW tbtjR owiJ sttii*. 

angles to the forward motion of the vessel, and is usually termed 
leeway. The centre of lateral resistance varies in position^ but 
it is approximately and sufficiently correct for all practical pur- 
poses at the centre of the immersed longitudinal section^ passihg 
through the middle line of the ship. In comparing pressures on 
sails to weights on a lever, it is not meatit that the actual sail 
acts as a weight, but rather the moment of the wind pressure on 
each sail, varying according to its distance from the centre of 
lateral resistance, has the same effect as a weight on a horizontal 
line in giving a bending or heeling moment. The next opera- 
tion is to find the centre of this wind pressure for all the sail 
area, or, as it is usually termed, the centre of effort. This is done 
by multiplying the area of each sail by the height of its centre 
from the centre of lateral resistance. Then the sum of all these 
moments, divided by the sum of the areas of all the sails, gives 
the vertical height of the centre of effort above the centre of 
lateral resistance. But it is also necessary to have the fore and 
aft position of the centre of effort, and this is obtained by multi- 
plying the area of each sail forward of the vertical line through 
the centre of lateral resistance by the distance of its centre from 
the vertical line. Having found the sum of all these forward 
moments, the same operation gives the sum of all the moments 
aft of the centre of lateral resistance. The difference between the 
forward and after moments, divided by the total sail area, gives 
the distance the centre of effort is forward or aft of the centre of 
lateral resistance. It will, therefore, be on that side on which 
the moments preponderate. (See position of centre of lateral 
resistance E, and centre of effort E, in fig. 124.) 

We might just notice here that when the centre of effort is 
before the centre of lateral resistance, the tendency of the vessel 
is to fall off from the wind. This is termed slackness. On the 
other hand, when the centre of effort is abaft the centre of lateral 
resistance, the tendency of the vessel is to fly up to the wind. 
This is termed ardency. 

In calculating the position of the centre of effort, only such 
sail as could safely be carried in a fresh breeze is calculated 
upon, and the sails are all supposed to be braced right fore and 
aft. A fresh breeze* is reckoned to blow with a force of 4 lbs. 
to a square foot of canvas. Thus the total sail area, multi- 
plied by the distance of its centre of effort above the centre of ^ 
lateral resistance, multiplied by 4 lbs., gives the moment of wind 
pressure in foot-lbs. For example, in fig. 124, if the sail area 
is 10,000 square feet, and the centre of effort above the centre of . 

* The pressure, equal to a fresh breeze, is taken from the British Meteoro* 
logical Office Tables. 



Sailing, sail ar^a, fiTc* 215 

lateral resistance is 50 feet, and the wind pressure on the sails 
is 4 lbs. per square foot, the heeling moment of the wind pressure 
is 4 lbs. X 10,000 square feet x 50 feet = 2,000,000 foot-lbs., or 

2,000,000 Qoo^ ^4. 
-? 1 =892 foot-tons. 

2240 

Now, supposing the displacement of our vessel to be 2000 
tons, and the metacentre above the centre of gravity, G M, to 
be 2 feet, what will be the angle of inclination with this force 
of 892 foot-tons wind pressure? We know that the moment to 
hold a vessel inclined at any angle is the righting lever of 
stability, GZ, multiplied by the displacement, D, = foot-tons. 
We have already got the foot-tons of heeling moment — viz., 892, 
so that 

?^ = GZ = -^ = 0-44GZ. 
D 2000 

We also know that GZ = GM x sine of the angle of heel 

G Z 

for small angles, so that --—-^ = sine of angle, 

GM 

•44 

— - = 0*22, sine of the angle of inclina- 

z 

tion, and reference to the table of natural sines at the end of 
this book shows the angle of inclination to be about 13**. 

The effect of setting top sails and top-gallant sails, and all 
such light sails, will now be evident. 

The higher the sail above the centre of lateral resistance, the 
more effect it has in producing large heeling moments, though it 
gives no increased propelling power. Thus, when signs of a 
squall appear, and all topsails are set, these are taken in first, 
for two reasons — 

1. If the vessel has a great metacentric height , and is, therefore, 
very stiff, when the squall strikes her she offers great resistance 
to heeling, with the result that, in such a case, the topmasts are 
often carried away, or the sails torn to shreds. 

2. If the ship is tender, and has, therefore, a small metacentric 
height, the effect of a squall of wind is to incline her to about 
twice the angle to which she would have gone if she had steadily 
and slowly inclined. Indeed, this would happen in any case. 
Many a vessel has been capsized through no other cause than 
this. A vessel with heavy yards, etc., is made stiffer by lower- 
ing these spare and stowing them on deck. The result is simply 
to lower the centre of gravity for the whole ship, and give 
greater metacentric height. 

A point deserving of notice here is, that as the vessel inclines, 
the effect of a horizontal wind pressure will not be so great aa 



2l6 ittJoW ifouil OWN sHii*. 

in the upright condition, since the surface upon which it blowd 
is at an angle less than a right angle. The same applies to sail 
which is not braced right fore and aft. However, our reasoning 
is sufficiently correct for all practical purposes, and the slight 
error, moreover, is on the safe side. Under such conditions, 
the angle of inclination is slightly less than it would other- 
wise be. 

Thus far we have simply considered the effect of a certain 
amount of sail in heeling a particular vessel with a given meta- 
centric height. But let us view the subject from a different 
aspect — viz., in determining some features in the design to carry 
a certain amount of sail at a given angle of inclination. From 
our previous consideration of the causes affecting metacentric 
height, we find that this may be done in two ways. It is known 
that great beam produces a high metacentre, and also, that in a 
deep vessel with comparatively small beam and low metacentre, 
the centre of gravity can be brought down by arranging the 
ballast to obtain the position of the centre of gravity required. 
The opinion is still in some degree prevalent that a vessel with a 
narrow midship section is better adapted for speed than one 
with considerable breadth. These erroneous ideas have been 
entirely upset by the valuable experiments conducted by the 
late Mr. Froude, who clearly showed that of two vessels of 
similar length and equal displacements, the one with the greater 
beam, and consequently of finer ends, was the better design for 
speed. At the same time, this design of vessel, with good beam 
and fine underwater form and ends, is the type which can be 
made stiffest and most capable of carrying great sail area, for it 
not only sends the metacentre high, but in yachts, by placing 
the ballast low, the centre of gravity can be brought down. 

Frictional Resistance. — From a point of speed, however, 
it must be remembered that short vessels encounter greater 
resistance from the friction of the water upon the immersed 
skin than long ones, the first 50 feet of length being the part which 
suffers most from frictional resistance. This is more especially 
so when high speeds are attained. After this length the particles 
of water, having partaken of the onward motion of the vessel, 
naturally offer a diminished resistance. Up to about 8 knots, 
from 80 per cent, to 90 per cent, of the total resistance is due to 
skin friction. 

The necessity, therefore, of keeping the bottoms of vessels 
clean is most important, as a rough surface adds immensely to 
the amount of resistance, a surface of the smoothness of calico 
offering approximately twice the resistance of a varnished siuface ; 
and, of course, sand about two-and-a-half times the resistance of 



SAttlKG, dAlL AB^A, Eil^C. 



217 




Vatnish. fieyond these speeds, other resistances become very 
important, frictional resistance diminishing to 50 per cent, or 60 
per cent, of the total. 

Wavemaking Resistance. — This is found most in vessels of 
bluff form at the ends, simply because, especially at the fore end, 
the head resistance offered by the bluffness, corresponding to a flat 
board moved as shown in fig. 125, causes the water to rise up in 
front of the vessel, and the making of this wave means expenditure 
and loss of power. It is not uncommon in vessels of the bluff 
cargo type, of not more than 9 knots 
per hour, to create a considerable wave 
6 or 8 feet in front of them. 

In vessels bluff at the after end, 
waves are also created at the stem, 
though not to such a marked extent ; 
but something else occurs which gives 
rise to another resistance — viz. : — 

Eddy-making Resistance. — ^This 
is similar to the effect of the flat board 
moved as shown in fig. 125. After the 
water has poured round the edges of 
the board it eddies behind it, and 
travels in the direction in which the 
board is moved. All the energy needed 
to produce this is loss of power. Just 
so is it with our actual ship. The 
eddying water being dead, the rudder 
is rendered less efficient, and if the 

vessel be a screw steamer the propeller is also less effective ; so 
^hat, while it is most essential for speed to have the entrance of 
the fore end fine, it is of paramount importance to have the run 
03;- the aft end fine, as there is the danger of a double resistance — 
wave and eddy-making — which for high speeds assumes enormous 
proportions. 

Coming back to the subject of design, let us take a yacht 100 
feet long, with a displacement of 200 tons, and a required sail area 
of 5000 square feet. This would represent, at the rate of 4 lbs. 
per square foot, a sail pressure from wind of 




Fig. 126. — Wave and 
Eddying made by Moving 
A Flat Board through 
Water, 



4 lbs. X 5000 
2240 



8*9 tons. 



Let the estimated height of the centre of effort above the centre 
of lateral resistance be 40 feet, then 40 x 8*9 = 356 foot-tons 
heeling moment. This must be balanced by the stability at, 
say, a required angle of inclination of 15°. 



Sl^ KNOW tOtJR oWn" mt^. 

First, we must find the righting lever of stability at' tliis 



angle — 



Displacement x lever, or G Z = moment, 



then, Moment ^ j ^^^^ 

Displacement 

therefore, ?5^ = 178 = GZ. 

200 

The next operation is to find the height of the metacentre, 
G M, above the centre of gravity, which will give 1*78 = G Z. 

The rule is, G M x sine of the angle of heel = G Z, 

then - . %^ . =GM, 

sine of angle 

the sine of IS** = 0-258 ; 

1*78 
therefore, — -—= 6*9 feet metacentric height. 

0-268 * 

In yachts there is the alternative, where the displacements are 
equal, as to whether it is better to get metacentric height by- 
beam, with more or less draught and less ballast, or by increased 
depth and draught, and less beam and more ballast. On this 
point, as the designs of recent fast racing yachts prove, naval 
architect experts differ in opinion in some degree. 

However, in sailing-ships, where it is not possible to regulate 
and fix the centre of gravity as on a yacht, whose conditions are 
fairly constant, but which, on succeeding voyages, carry cargoes 
of varying densities, it becomes necessary to give sufficient meta- 
centric height and stiffness by means of beam. 

In some cases double bottoms are fitted for water ballast, but 
this is not the common practice, since, when the holds are full and 
the tanks empty, the effect of the double bottom is to raise the 
centre of gravity of the cargo, and tend to make the vessel tender. 
The combined effect of lofty masts and great sail area unite to 
necessitate greater stiffness. 



SiPAfetLiTt It^FORlktADtoK. 



SIS 



C it AFTER Vl. (Skction VIIL) 



STABILITY INFORMATION. 



What stability information should he supplied to a commanding 
officer? 

It would be rather a difficult matter to answer this question 
to the satisfaction of every naval expert, and non-expert, since 
the purposes for which vessels are built vary so much in their 




30' •♦o* so' 
Scale of Degrees. 

A, Curve for fully equipped condition. 

B, Curve for coal and stores consumed. 



70' 



SO' 



—I 
90' 




Angle of Maximum Stability. A, condition. 
Fig. 126.— Curves of Stability of a Steam Yacht. 

nature. But it appears that the commanding officer, after 
making himself thoroughly acquainted with the principles of 
the subject, and fully aware of the possible exigencies which his 
vessel may meet, is the fittest and most capable person to decide 
what information is required. It is scarcely necessary at this 
stage to state that officers of all vessels do not need the same 
information. In the case of a yacht whose condition is practically 



220 KNOW tOUR OWN SfilP. 

constant, the only change arising from the consumption of bunkeif 
coal and stores, scarcely any iiiformation is required, as such a 
vessel can be designed and built to fulfil certain conditions and to 
possess a definite amount of stability. At most, therefore, two 
curves, showing her righting levers and range, in the light and 
equipped condition, can be of any value in satisfying her captain 
of her reserve safety. Fig. 126 represents the curves of a steam 
yacht 152 feet long, 22 feet beam, and 13 J feet deep. 

Then, again, other vessels are built for special trades, and the 
exact natures and densities of their cargoes being thoroughly 
understood, the naval architect is able to produce a design such 
as will ensure certain conditions of seaworthiness in the loaded 
condition. 

But by far the majority of vessels are built to carry miscel- 
laneous cargoes, those known as tramps carrying anything and 
everything, anyw^here. So that while it is impossible to design 
and build a ship specially adapted for every trade, it lies in the 
power of the naval architect or shipbuilder to provide such 
information as will greatly help the conmianding officer in under- 
standing what condition of loading and ballasting to avoid, and 
what to adopt, to best make his particular vessel seaworthy. 
The method of supplying curves of stability, adopted by Messrs 
J. L. Thompson & Sons, Ltd., of Sunderland, is certainly a most 
commendable one. Figs. 106 and 107 show sets of curves provided 
by them for two of their steamers. 

In addition to the information on these curves in the case of 
general carrying vessels, there might be provided with great 
advantage and profit to the ships' officers the following, viz. : — 

(V) A curve of stability wJien floating at the load draught with 
the least metacentric height compatible with safety, as a guard 
against making the vessel too tender. 

(2) -4 curve showing the stability ivhen loaded to tlie hatches with 
the lightest homogeneous cargo likely to be carried of specified 
density or cubic capacity per ton, with a statement of the amount 
of ballast to be carried in order to ensure safety and produce the 
best behaviour. (But it does not follow that the vessel should be 
ballasted down to her load waterline to obtain such a condition.) 

(3) ^ curve of stability with the heaviest cargo likely to be 
carried of specified density or cubic capacity per ton weight, 
together with a statement of how such cargo should be stowed 
in the holds and 'tween decks, so as to ensure sufficient stability, 
and the best behaviour at sea. 

(4) An intermediate cutuefor a cargo of medium density y and a 
statement of the quantity of ballast, if such is required, to pro- 
duce the best results. 



STABILITY INFORMATION. 221 

(5) A most important curve is that showing the best condition 
of a vessel light and in ballast, with an exact statement of the 
amount and position of ballast to be carried to ensure such a 
condition. . 

In these days, when water ballast is so extensively used, a 
great amount of ignorance is evinced as to how and where it 
should be stowed to secure the desired results. In some cases 
water ballast is carried only in fore and after peaks, with as little 
temporary ballast as possible in the holds. The effect of this 
in straining the vessel has already been pointed out. The 
commonest method is to fit water ballast tanks throughout the 
whole or part of the length of the bottom, and to fill them all 
up when light, regardless of the diffierence in type, proportions, 
etc., and the result is that officers often have to complain of 
their vessels almost rolling their masts overboard. A glance at 
figs. 106 and 107 very clearly indicates what would be the 
probable behaviour of these vessels at sea, light or with their 
ballast tanks full. Curves A and B show the stability levers of 
the vessels light, and C and D with the ballast tanks full. In 
all these cases, and especially in fig. 107, the levers are very 
long for small angles of inclination ; in fact, the vessels have too 
much stability, with the natural and consequent result that 
heavy rolling would most probably be experienced. We are 
thus driven to the truth that the bottom of the ship is not 
always the proper place for all the ballast. As previously 
explained, a better principle sometimes adopted is to fit very 
deep tanks in the region of amidships, which, while increasing 
the displacement, also mitigates the evil of excessive stability. 



222 KNOW TOUR owjir shi?, 



CHAPTEK VL (Section IX.) 

CLOSING REMARKS ON STABILITY. 

General Results. — Before concluding our considerations of the 
various aspects of the subject of stability, it may be advisable 
to gather up, as briefly as possible, a few of the most important 
facts which have been revealed. 

The centre of buoyancy is the centre of gravity of the displaced 
water, at whatever angle the vessel may be inclined, and tlm)ugh 
which the upward vertical pressures of buoyancy act. 

The transverse metacentre is the point where the vertical line 
through the centre of buoyancy for indefinitely small angles of 
inclination intersects the middle line of the vessel (such middle 
line being the line through keel and masts), and is also the point 
above which the centre of gravity must not rise, in order that 
a condition of stable equilibrium may be maintained. It is 
influenced chiefly by beam. 

The metacentre and the centre of hvxyyancy vary in position 
with every variation of draught, but always occupy the same 
respective positions at any particular draught. Their exact 
positions, when floating upright at any draught, are found from 
curves obtainable from the shipbuilder or naval architect. 

The centre of gravity is the centre of the total weight (not 
bulk) comprising a ship and her entire equipment and cargo. 
It may, therefore, occupy widely different positions for the same 
draught, according to the high or low positions of the weights 
carried. The centre of gravity is found by experiment, as pre- 
viously explained in this chapter. 

The distance between the centre of gravity and the metacentre 
is termed the metacentric height. 

Metacentric height in feet, multiplied by the sine of any angle 
not exceeding 10° or 15° for ship-shaped vessels, gives approxi- 
mately the righting lever of stability, in feet, for that angle. 
Righting lever in feet, multiplied by displacement in tons, equals 
rig] 1 ting moment in foot-tons. 

Metacentric height, or metacentric stability, is held to be 
unreliable beyond the small angles previously stated, as it may 
continue to grow both in the length of the levers and in the 



CLOSING EBMABKS ON STA6ILITT. 22B 

extent of the range, or it may rapidly decrease and vanish 
altogether^ 

The lefoer of stability can be ascertained at any angle of inclina- 
tion by finding the position of the centre of buoyancy at that 
angle. The horizontal distance between the vertical lines 
through the centre of buoyancy and the centre of gravity indi- 
cates the righting lever. If the vertical line through the centre 
of buoyancy intersects the centre line of the vessel (that is, the 
line passing through the keel and masts) above the centre of 
gravity, the lever is a nghting one ; if it intersects below the 
centre of gravity, the lever is an upsetting one. 

A diagram, showing the levers of stability at all angles of 
inclination when in any particular condition, indicating both 
the angles of maximum levers and vanishing point of stability, 
is termed a curve of statical atahility^ and is also obtainable from 
the naval architect or the shipbuilder. 

Large metacentric height indicates great stiffness^ and small 
metacentric height tenderness. 

Stiffness can be obtained in designing a ship by increasing 
the beam, and thereby raising the metacentre ; and in an actual 
vessel already built, by lowering the weights on board and 
bringing down the centre of gravity. 

If the range of a vessePs stability is known at the load 
draught with a certain metacentric height, any reduction in 
that height, which can only be effected through the centre of 
gravity, means reduced range and reduced levers of stability, 
and any increase produces both increased level's and range. 

Similar metacentric heights at different draughts produce 
widely different conditions of stability. 

Freeboard is also a powerful agent in influencing a vessel's 
stability, but by itself is no guarantee for either the range or 
the length of righting levers. The greater the freeboard, com- 
bined with a fixed position for the centre of gravity and a fixed 
draught, the longer become the righting levers at considerable 
angles of inclination, and also the greater the range. 

At light draughts, even good metacentric height (such as 
might be admirably adapted for load draught) and great free- 
board may only produce small range and levers of stability. 

Great stiffness creates rapid movements among waves, and 
tends to heavy rolling, while tenderness conduces to slow, easy 
movements, and general steadiness. 

All vessels endeavour to float among waves in a position 
perpendicular to the wave surface. How far they succeed, de- 
pends chiefly upon the ratio of their period of oscillation in still 
water to the period of the waves among which they are moving. 



224 KNOW YOUR OWN SHIP. 

By a vessel's period of oscillation -is meant the time taken to 
perform one complete roll, that is, say from port to- starboard^ 
when forcibly inclined in still water. The period for large and 
small angles of roll is approximately the same. 

By the wave period is meant the time occupied in the passage 
of two successive wave crests past a stationary object. 

When the period of oscillation is less than half the wave 
period, the vessel will roll with the waves, approximately main- 
taining herself perpendicular to their surface, being upright at 
their summit and trough, and at her greatest inclination on the 
steepest part of the wave slope. This could only be accom- 
plished by vessels of extraordinary beam to depth, and also 
when the beam is comparatively small in relation to the length 
of the waves, but is exactly the manner in which a small raft 
would float among waves. 

Although it is most uncommon to find vessels so rapid in 
their movements as to have their period of oscillation less than 
the half wave period, it is not so uncommon to find vessels 
which have been made so stiff" as to have a roll period of probably 
half the period of the waves they are likely to fall in with, pro- 
ducing s^ynchronism with the waves, or, in other words, keeping 
time, and thus when at their greatest angles of inclination, they 
receive the impulse of the wave, they answer by taking a 
tremendous lurch. 

Synchronism may also occur periodically on a series of waves. 

When it is remembered that waves in different localities, and 
at different times, vary both in length and period, it will be seen 
that it is scarcely possible to always escape the effect of 
synchronism, however a vessel may be loaded. It should be 
noted that in vessels made excessively stiff", the probability of 
synchronism is greatly increased, and on the other hand, with 
the slow rolling ship, though it is not imlikely that occasionally 
she may fall in with waves producing the same effect, neverthe- 
less, taking her all round, she is certainly the steadier and more 
comfortable ship. 

Slow rolling motion^ which is conducive to steadiness, may be 
obtained chiefly in three ways : — 

1. By small metacentric height. 

2. By means of resistance agents on the immersed skin in the 
form of bilge keels. 

3. By winging out the weights from the centre to the sides of 
the vessel. 

The two latter of these are very safe methods, since they make 
no deduction from the vesseVs stability. The first, however, 
necessitates a correct understanding of the vessels dealt with. 



CLOSING BBMABKS ON STABILITT. 225 

for, as previously stated, any reduction of metacentric height 
produces both shorter levers and range. Moreover, what is 
safe and good for one ship may be exceedingly dangerous for 
another, hence the necessity of correct information being pro- 
vided by the designer, and received by the commanding oflBcer, 
in order to ensure safety. 

Synchronism among waves upon a vessel of very small meta- 
centric height and slow rolling period may cause her to reach 
large angles of inclination, and if the levers and range are very 
short, will greatly increase the possibility of her capsizing. 

Bad loading may thus produce both the dangerous extremes — 
excessive stiffness with heavy rolling, and too much tenderness 
with great lack of necessary stability. 

Synchronism may be destroyed by altering the speed or 
course. 



226 KNOW YOUR OWN SHIP. 



CHAPTER VII. 

TRIM. 

Contents. — Definition— Moment to Alter Trim — Change of Trim — Centre of 
Buoyancy of Successive Layers of Buoyancy at Successiye Draughts — 
Longitudinal Metacentre — Longitudinal Metacentric Height — Moment 
to Alter Trim One Inch — Practical Examples showing how the Change of 
Trim is Ascertained. 

Under certain circumstances — cases of emergency, accidents to 
propeller and shafting, entering docks, etc., it often becomes 
necessary to decrease the draught of a vessel with or without an 
alteration to trim, or to simply alter the trim by putting the ship 
down by the head or the stern as may be required. (Trim is the 
difference between the draughts as indicated at the stem and 
stem.) 

Trim is a subject of e very-day consideration to the scientific 
designer, and is so inseparably related to stability that, in order to 
obtain the best results, they must be dealt with simultaneously. 
However, in dealing with the subject it is assumed that due 
regard has been paid to stability in the vertical distribution 
of the weights of the cargo, and our attention is directed to the 
longitudinal distribution of weights, whether they be in the form 
of cargo in the holds, or water in the trimming tanks. 

Sometimes, in a specification for a new vessel, a shipowner 
inserts a clause to the effect that his vessel when loaded with a 
homogeneous cargo, must trim in a certain condition, say, 1 foot 
by the stem. 

At first sight this might appear an awkward condition for a ship- 
builder to guarantee. But with a thorough grasp of the principles 
of buoyancy and gravity it is very simple, though it may entail 
considerable labour and time in order to get an accurate result. 

Where a high speed is required, the under-water form of the 
vessel is designed to the stipulated draught regardless of internal 
arrangement of holds, position of engines and boilers, etc. When** 
this is completed, having secured the displacement required and 
the best form of lines for high speed, the longitudinal position of 
the centre of buoyancy is calculated, and the designer knows that 
the weights constituting the hull and equipment of the ship, 



TRIM. 227 

including engines and boilers, and the holds loaded with homo- 
geneous cargo, must be so arranged that the centre of gravity of 
the whole must be vertically over the centre of buoyancy. When 
such a condition is fulfilled, no doubt rests as to the trim of the 
ship when she is built and loaded. 

Everyone knows that to shift a weight forward or aft along a 
ship's deck will produce some alteration to the trim. If the weight 
is moved forward, as in fig. 127, where 10 tons are shifted 60 feet, 



Fig. 127.— Change in Teim oaitsbd by moving a Weight 

FORWARD ALONG A Sh1P*S DeOK. 

the vessel must have increased in draught at the stem, or, as we 
say, "gone down by the head," and, consequently, as the mean 
draught remains practically the same, she must have risen by the 
stem. As the effect upon the trim for a particular ship at a 
certain draught depends almost entirely upon the amount of the 
weight and the distance it is moved, the moment obtained by 
multiplying the one by the other (10 x 60 = 600) is termed the 
" moment to alter trim" However, this quantity gives little idea 
as to what the exact change in trim will be, especially when it is 
remembered that the same moment will produce different results 
at different draughts, and by itself it is therefore practically use- 
less. Could we discover a moment that would give 1 inch change 
in trim at the required draught, then the problem is solved, for it 
would be simply a matter of finding how often the moment to 
change trim 1 inch could be got out of the total moment to alter 
trim, and the result would be change of trim in inches. 

It should be clearly understood that " change of trim " means 
the change in draught at stem added to change at stem and vice 
versa. A ship floating at, say, 10 feet draught forward and 11 
feet aft, changes trim owing to the shifting of weights on board 
and the new draught is 10 feet 1 inch forward and 10 feet 11 
inches aft. She has gone down 1 inch by the head and risen 1 
inch by the stem. The change in trim is 2 inches. 

How to obtain the moment to change trim 1 inch we shall 
investigate shortly. 

Let fig. 128 be a ship floating at the waterline a b. The centre 



228 KNOW TOUR OWN SHIP. 

of buoyancy is at R One condition for a vessel to float in a state 
of equilibrium is that the centre of buoyancy and the centre of 
gravity be in the same vertical line, considered both transversely 
and longitudinally. If this be a ship's condition as regards the 
transverse centre of buoyancy, and with the metacentre above the 
centre of gravity, she floats upright in a condition of stable 
equilibrium, and the vessel will incline to neither one side nor the 
other, except by the application of exterior force. Sometimes, 




.^ 



t 



.B 



1 



Fig. 128. — Illustrating the Alteration in the Fore and Ajt Posi- 
tion OF THE Centre of Buoyancy of the Suoobssive Laybbs ov 
Buoyancy caused by Increased Immersion. 

however, probably owing to the shifting of weights on board, the 
ship will only And a condition of rest after she has inclined to an 
angle of greater or less degree ; in short, till the centre of gravily 
and the centre of buoyancy are again in the same vertical line. 

When a vessel is launched, she at once seeks a position of rest 
such as we have described. Transversely, she most likely floats 
upright, but, looking at her fore and aft, we often find that she 
heels, perhaps several degrees either towards the stem or the stem, 
or, as we say, " trims " either by the stem or the stem. 

Let fig. 128 represent the condition of a ship just launched, 
trimming, say, 2 feet by the stem at waterline a b, and B is the 
fore and aft centre of buoyancy. It is clear, then, since the vessel 
floats in a condition of equilibrium, that the centre of gravity is in 
the same vertical straight line as the centre of buoyancy, and thus 
we at once have the longitudinal position of the centre of 
gravity. 

Suppose we wish to load such a vessel without altering the 
trim. Naturally the draught increases as the loading proceeds. 
The question is : — Where should the additional weight of the 
cargo be placed 1 and it is exactly at this point where many 
blunder. The assumption often worked upon is, that the centra 
of gravity of the added weight should be placed in the same 
vertical line as the centre of gravity and the centre of buoyancy 
when floating at the original draught. Were a ship as regular 
in shape as a box, such an assumption would be quite right; 
but for ships it is utterly wrong, for were such a method carried 
out, it is not at all unlikely, in many cases, that the trim would 

\ 



TRIM. 229 

have altered — the reason is not difficult to ascertain. Let us 
suppose that the cargo has to be loaded in four instalments of 
equal weight, putting the vessel down successively to the water- 
lines cd, e/, g h, j k. Though B is the fore and aft position of the 
centre of buoyancy at the waterline a b, it does not follow that it 
will occupy the same fore and aft position at the waterline c d. 
If the ship trims considerably by the stern, it may be found that 
the centre of buoyancy of the layer of displacement between the 
waterlines a b and c d may be some distance aft of B, so that to 
immerse this buoyancy, the centre of the added weight must be 
placed over the centre of its own particular buoyancy B' or equally 
distributed on each side of B'. Similarly, the centre of buoyancy 
of the next layer of displacement may not be over either B or B^, 
but at B^, and thus the next instalment of cargo must be placed 
over B2 in order to put the ship down bodily and not alter the 
trim, and so on up to the load waterline. 

In order to make further comprehensive these counterbalancing 
forces of weight and buoyancy, let us take another illustration. 
Suppose our ship to be floating at rest in a light condition at the 
waterline a b, fig. 128. The centre of buoyancy is at B, and the 
centre of gravity is at a point vertically above it. Here we have 
the whole weight of the empty ship supported by all the buoyancy 
below a b. One hundred tons of cargo in quantities of 10, 15, 30, 
20, and 25 tons are to be placed on board in such positions as to 
cause no alteration to trim, the vessel having to float at the water- 
line c d, which is parallel to a b. It is evident, therefore, that 
the volume between a b and c d must measure 100 tons of floating 
power or buoyancy. So that what we have to deal with is 
not the original buoyancy below a b, nor the light weight of the 
ship. These drop out of our consideration altogether. Our 
attention is directed to the 100 tons of weight, and the 100 tons 
of buoyancy which has to support it. Let B^ be the centre of this 
100 tons of buoyancy; the centre of the 100 tons of cargo must 
be placed in the vertical line which passes through B^, it matters 
not whether the weights be on deck or in the bottom of the hold, 
the centre only must be, as stated, in the same vertical line with 
BK 

Let us proceed to load. 



The 10 tons 


are 


placed 5 feet abaft of B^ 


)) 


15 


>» 


80 


1) 


it 


80 


i» 


24 


II 


>} 


20 


II 


40 „ 


forward „ 



The question arises, " Where should the 25 tons be placed in 
order to get the vessel to the trim required *{ " 



230 KNOW YOUR OWN SHIP. 

Moments aft. Moments forward. 

10 X 5 = 50 20 X 40 = 800 foot-tons. 

15 X 30 = 450 
80 X 24 = 720 

1220 foot-tons. 

1220 - 800 = 420. 

We still require a moment forward of 420 foot-tons in order to 
equalise the moments of each side of B\ and this has to be 
obtained by placing the remaining weight of the cargo, 25 tons, in 
such a position as to produce this. 

Weight X distance from B^ = moment in foot-tons, therefore, 

— ;-T- - = distance from B^ that the 25 tons must be placed, 
weight 

^ = 16-8 feet, distance required. 

To the average ship's officer considerable difficulty presents 
itself in carrying out a method such as that just described. He 
asks, how is he to find the centre of buoyancy of the layer of 
buoyancy which is immersed, owing to the addition of a certain 
weight. It is true that there are ships* officers who, far ahead of 
their profession in the knowledge of ship theory, have had them- 
selves provided with the lines plans of their ships, from which 
they can ascertain the form of the whole or any section of their 
vessels. Without such a plan the centre of buoyancy of any 
particular layer of buoyancy could not be found. However, it 
is not intended to propose any such process as an every-day, 
practical, handy method for seamen. But, imderstanding the 
fiuidamental principle, a simple, practicable, and reliable method 
may be deduced. Where the increase in draught is not very 
great, instead of finding the centre of buoyancy of such a layer as 
that between a b and cd in fig. 128, it is sufficiently correct for all 
practical purposes to find the centre of gravity of the waterplane 
a &, and take this as the approximate position of the centre of 
buoyancy. From this point calculate the moments of the weights 
of cargo placed on board. Here, again, for any seaman to have to 
calculate the centre of a waterplane,* whenever he desired to 
estimate the trim, would be out of the question. But the second 
difficulty can readily be overcome, for just as easily as a curve of 
displacement, or a curve of " tons per inch " is made, can a curve 
of centres of gravity of waterplanes be constructed, and, by this 
means, the centre of any waterplane between the light and load 
draughts can be ascertained. This could, with little trouble and 
at the expense of little time, be supplied by the shipbuilder or the 

* Rules for exact calculations and worked examples are found in Chapter X, 
on " Ship Calculations," 



231 



Curve 1, fig. 129, is euch a curve for a steamer 352 
J a feet by 28 feet. ITie vertical scale represents draughts, 
the horizontal scale, distances of centre of gravity of waterplanes 
from after aide of after stern-post. 

It must be understood that all centres of gravity so found will 
be for waterplanes parallel to the keel only, and are only strictly 
correct when taken for a vessel floating upon even keel. When a 
ship trims slightly by the stem or the stem, the result* obtained 
by using the distances from this curve would be practically correct. 











BoIeotD 


etu 


cet 


from alUr .Ide of 8lam-Po.t. 














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H»« MiWMjBjaljWOTWa 


,«-»» 1 






















































































1 








31 






































1/ 














































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m 






































u 






i 


W 






































U 












































n 








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w 






































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Fio. J2B.— CuEVBa OF Cbiitebs ot GaAvirr of Watirplaweb. 
No. 1. Oh Even Keel. 

No. 2. TeIMMINO a FEET B^ THE STEBH. 

Where, however, a vessel trims very much by the stem, these 
distances may be considerably in error. In order to come nearer 
the truth, it might be advisable to have another curve, No. 2, on 
our dii^;ram, calculated for the same mean draughts, but with the 
ship trimming 6 feet by the stem. This curve would show the 
centres of gravity further aft. With these two curves, and the 
exercise of a little judgment, it is possible to fix the position of the 
centre of gravity of any waterplaiie in any condition of trim with an 
exactitude amply sufficient for all practical and working purposes. 
Let it be understood that when only a weight already on board 
is shifted, the moment altering the trim is simply the product of 



232 KNOW YOUR OWN SHIP. 

the weight and the distance it is shifted. But when a weight or 
weights are placed on board in certain positions, or are taken out 
of a ship, then these weights are multiplied by the distance between 
their centres and the centre of the waterplane. If the weights are 
placed forward of this point, then the moment obtained tips the 
ship forward ; if the weights are aft, the moment tips the ship aft. 
If some of the weights are placed aft and some forward, then the 
difference between the fore and aft moments gives the moment 
altering the trim. When weights are discharged from a ship for- 
ward, the result is a moment putting her down by the stem, and 
vice versd when weights are discharged aft. Naturally, discharging 
weights decreases the mean draught, while alteration to trim may 
also be caused. 

The centres of gravity of the waterplanes, from which are 
taken the distances in order to get the moment to alter trim, 
have been very aptly called the " tipping centres," and in future 
we shall adopt this handy and expressive term. 

Having, it is hoped, made clear how to ascertain the moment 
to alter trim, our next step will be to find what the exact altera- 
tion to the trim is. 

When a ship is moderately inclined transversely, the stifihess is 
measured by the metacentric height, and thus, the greater the 
metacentric height, the less inclination will be caused by the 
transverse shifting of a weight on board. A vessel, considered 
either transversely or longitudinally, will have the centre of gravity 
at the same height from the keel, in any particular condition of 
loading or ballasting. The centre of buoyancy also is at the same 
height in both cases. 

But, in turning to the metacentres, there is a great diflFerence 
in their positions. Transversely, the metacentre Varies from a 
few inches to a few feet above the centre of gravity for passenger 
and cargo steamers. But longitudinally, for the same vessel, it 
may be as high, or higher, than the vessel is long. 

Metacentre above centre of buoyancy 

_ Moment of Inertia of Waterplane. 
~ Displacement in cubic feet. 

We have only one displacement, as we have only one ship 
with which to deal, so that the diflference must lie in the moment 
of inertia of the waterplane. And yet we have only one water- 
plane, and one area for both transverse and longitudinal considera- 
tions. Then it is evident that the moment of inertia for longi- 
tudinal inclination cannot be similar to the moment of inertia for 
transverse inclination, and this is so. 



TRIM. 



233 



For transverse inclination, the moment of inertia is calculated 
about the fore and aft middle line of the particular water- 
plane. For a rectangular waterplane the moment of inertia is 
Length x Breadth^ 

12 • 

But for longitudinal inclination, the moment of inertia is 

calculated about the transverse axis passing through the centre of 

gravity of the same waterplane, and for a rectangular figure the 

. « . _^. ij , Length^ x Breadth 
moment of mertia would be ^ — . 

Taking the length of a rectangular waterplane as 100 feet and 
the breadth 20 feet the moment of inertia for transverse inclination 
would be 6 6 6 6 6 (draught 10 feet), and metacentre above centre 




Fig. 130. 

of buoyancy, 3 '3 feet ; and for longitudinal inclination, 16 6 6 6 6 6, 
and metacentre above centre of buoyancy, 83*3 feet. This enormous 
longitudinal stifihess possessed by ordinary cargo and passenger 
vessels explains why they are so much more easily inclined trans- 
versely than longitudinally, either by the application of exterior 
force, or the shifting of weights on board. Let fig. 130 represent 



234 KNOW YOUR OWN SHIP. 

a vessel floating at the waterline "W L, in which condition G is 
the centre of gravity, B the centre of buoyancy, and M the meta- 
centre. A weight at P is shifted horizontally a distance of d to 
T. The vessel alters trim so that W^ L^ is the new waterline, B^ 
the new centre of buoyancy, and G^ the new centre of gravity 
which has travelled in a direction parallel to a line joining the 
centre of the weight in the original and new position. The 
vertical line through B^ and G^ intersects the originally vertical 
line through B and G at M, the metacentre. Let the waterplanes 
intersect at the point O, which for moderate inclinations is the 
tipping centre. Here we have now three triangles G M G^, 
W W^, L L^, whose angles are similar. 

G Gi = ^. , P X ^ . 

Displacement in tons 

G G^ also = G M X tan angle M, 
then tan of angle M = or 



G M D X GM 

D = displacement in tons. 

Similarly in triangle L O L^ we have : — 
L L^ = O L X tan of angle 0, but angle O = angle M, 

therefore L L^ = L x _ , ■ or 



G M D X GM' 
and similarly in triangle W W^ we have 
W Wi = W X tan of angle 0, 

or W Wi = W X -^-^^JL, 

D X GM 

And for a total change of trim we have 

W Wi + L Li - W L tan of angle 

Assuming that a certain weight P moved a certain distance 

gives 1 foot change of trim, then -— ofFxd will equal the moment 

1^ 

to alter the trim 1 inch, and this is the moment it is usual to find. 

The formula will now be : 

1/wT V X d \ ^ , DxGM 

— I W L X I or P X a = = moment to 

12 V DxGM/ W L X 12 "'"""*'"*' "^ 

alter trim 1 inch. 

The only factor in this formula for moment to alter trim 1 
inch which presents any difficulty to a ship*s officer is G M — the 
longitudinal metacentric height.* But this can be overcome by 

* See Chapter X. for rules for the calculation of the height of the longi- 
tudinal metacentre. 



TBIM. 255 

obtaining from the builders or deBigners a curve of longitudinal 
metacentres. This is interpreted in exactly the same manner as 
the curve for transverse metacentres. Fig, 131 is such a curve. 

Knowing the position of the centre of gravity in a light, and 
perhaps one or two other conditions, it will be an easy matter to 
roughly approximate the position of the centre of gravity in any 
other condition. With so great a distance between the longi- 



J \ 


J \ __ 


.L_____\-- 


i \ 




M n V m: T. SI js m jbjt h am a t 



Sole o( DnughtB. 

FiQ. 131. — Cttbve of Lonoitudinal METAOENTBaa. 



tudinal mefacentre and the centre of gravity, an error of a foot or 
so in approximating the position of the centre of gravity would 
make practically little difference in the final result. A few 
examples are now given illustrating the application of these 
methods. 

To calculate the effect upon the trim of filling or emptying 



236 KNOW YOUR OWN SHIP. 

trimming tanks, the centre of gravity of each separate tank ought 
to be known ; this could easily be supplied by builders, together 
with the exact capacity of each. The same remark applies to the 
filling and emptying of bunkers. 

Example I. 

A ship is 352 feet long. The displacement is 6200 tons on a 
draught of 20 feet aft and 18 feet forward. The mean draught 
is therefore 19 feet. At this draught, it is found by referring to the 
metacentric diagram (tig. 131) that the metacentre is 460 feet above 
the keel. By approximation, the centre of gravity is 16 feet 
above the keel. 460 - 16 = 444 feet metacentric height. The 

length of the waterline is about 352 feet. Then ^^^ — — = 651 

^ 352 X 12 

moment to alter trim 1 inch. 

One hundred tons of cargo are taken out of an after-hold and 
placed in a fore-hold, the distance moved being 100 feet. 

Required — alteration to trim. 

100 X 100 = 10,000 = Moment to alter trim. Then 

- '--— = 15J ins. = Total change of trim. 
651 * 

Should the tipping centre be at or near the middle of the length, 
then the amount of immersion at the fore end and the amount of 
emersion at the after end will be equal, the draught forward 
being 18' 0" + 7| = 18' 7|", and aft 20' 0" - 7f" = 19' 4f". 
However, as previously shown, this could be ascertained with 
considerable accuracy by referring to the curves of centres of 
gravity of waterplanes. 

It is found, ^g. 129, that the tipping centre is 175 feet from the 
after side of the stem-post, and it will be 177 feet from the fore 
side of the stem. Under such circumstances the inunersion at the 
fore end and the emersion at the after end will be practically equal. 
Where the difference is considerable the immersion and emersion 
at the ends is proportional to the two lengths making up the whole 
length of the w^aterline. 

Supposing an error of 2 feet had been made in estimating the 
position of the centre of gravity, and instead of the metq,centric 
height being 444 it should have been 442, the effect upon the total 
alteration of trim would have been less than ^ inch, which in 
practice would not be a serious error. 

Example II. 

We will take the same vessel \mder similar conditions, floating 
at the same original draught, 20 feet aft, 18 feet forward. 



TRIM. 237 

Suppose we were asked how far to shift the 100 tons forward 
to bring the ship upon even keel. That is, the trim has to be 
altered 24 inches. 

We found that the moment to alter trim 1 inch was 651, 

therefore the moment for 24 inches will be 24 x 651 = 15624, 

15624 

= 156 feet, distance 100 tons has to be moved forward. 

Example III. 

Again, taking the same vessel floating at the same waterline 

under the same conditions, let the main double bottom tank 

now be filled. The tank contains 210 tons of water. Required — 

the effect upon the trim. It is clear that the draught must 

have increased. In making the estimation for alteration to 

trim caused by placing a weight on board a ship, it is always 

assumed that the weight is first placed over the centre of gravity 

of the waterplane at which the vessel is floating. This, as we have 

seen, increases the draught uniformly, when the weight is small 

compared with the displacement of the ship. The weight is then 

shifted to its proper position, and the alteration to trim found, as 

shown in the foregoing examples. Referring to the scale or curve 

of "tons per inch," which, along with capacities and deadweight 

scales, is often, or should be, supplied to ships, the tons to increase 

draught 1 inch is found. Let the " tons per inch " be 30, then 

210 

""— = 7 inches increase in draught by filling the tank. 

The new draught is 18 feet 7 inches forward, and 20 feet 7 inches 
aft. At this draught, we find, from the curve of longitudinal 
metacentres, the height of the metacentre, and again we approxi- 
mate the position of the centre of gravity, taking account of the 
210 tons in the bottom tank. 

The metacentric height is now 434. 

Then = 658 moment to alter trim 1 inch. 

352 X 12 

The distance from the centre of gravity of the tank to the 

tipping centre is 60 feet. Then, 210 x 60 = 12600 =» moment to 

alter trim. 

— -— =19 inches total alteration to trim. 

Supposing the ratio of the length of the waterline before the 
tipping centre to the length abaft be as 8 to 7, then the alteration 
to draught at each end of the vessel will be 10 inches forward, and 
9 inches aft, and the ultimate draught will be 18' 7" + 10" = 19' 5'' 
forward, and 20'-7" - 9" =- 19'-10^ aft. The effect upon trim of 



238 KNOW YOUR OWN SHIP. 

loading a moderate quantity of cargo or filling bunkers would be 
calculated in a similar manner. 

Example IV. 

Again, taking the same vessel, it is desired to find the effect 
upon trim caused by consuming 200 tons of coal out of a cross 
bunker. In this case we first assume in calculation that the 
200 tons of coal are carried from the cross bunker and placed 
vertically over the tipping centre, and the alteration to trim is 
then found. Let the 200 tons be situated in a bunker 30 feet 
forward of the tipping centre. The moment to alter trim 1 inch 
we found in Example I. to be 651, and the moment to alter trim 
is 200x30=6000. 

— — - = 9 inches total change of trim. 
651 

Let it again be divided in the proportion of 8 to 7 = 5" and 4". 
The draught will be 18' 0"-5" = 17' 7" forward, and 20' 0" + 
4" = 20' 4" aft. 

It is now assumed that the 200 tons weight is lifted from its 
l)osition in the vertical line passing through the centre of gravity 
of the waterplane, and got rid of (consumed). The draught 
will be decreased uniformly all fore and aft. The " tons per inch " 
is 30. 

o'A = ^i" decrease in draught, and the ultimate draught is 17' 7" - 

6f" = 17' OJ" forward, and 20' 4" - 6f" = 19' 9 J" aft. 

Where a moderate quantity of cargo, or water in trimming tanks, 
is discharged, the effect upon trim is found similarly to the method 
given for consumption of bunker coal.* 

For further illustrations and actual trim calculations see 
Chapter X. 

* With the aid of such diagrams as proposed, the efifect upon trim of 
loading lar^e quantities of cargo, or other weight, producing considerable 
increase in draught would be calculated in a very similar way. 

1st. Find increase in draught parallel to present draught from displace- 
ment scale. 

2nd. Find position of centre of buoyancy of new layer of displacement 
from curves of tipping centres. 

3rd. Distribute cargo into intended positions in holds. 

4th. Ascertain moment to alter the trim. 

5th. Ascertain moment to alter trim 1 inch at this new load-Une, then 

— r^ = Alteration of trim. 
5th 



TONNAOB. 239 



CHAPTER VIII. 

TONNAGE. 

Contents. — Importance to Shipowners from an Economical Point of View — 
Under Deck Tonnage — Gross Tonnage — Register Tonnage — Deductions 
for Register Tonnage — Importance of Propelling Deduction in Steamers 
— Deep Water Ballast Tanks — Deck Cargoes — ^Examples of Actual Ship 
Tonnages — Sailing Vessels— Suez Canal Tonnage — Yacht Tonnage. 

MERCHANT VBSSBLS. 

Importance to Shipowners. — Ships' dues, such as pilotage, 
dock, river, etc., are paid upon the register tonnage. Tonnage 
is, therefore, a subject of great importance to the shipowner, 
from an economical point of view. Nevertheless, considerable 
misunderstanding is prevalent as to what tonnage really is. 

Register tonnage does not, as some would imagine, give any 
idea of the size of a vessel, for, an ordinarily proportioned vessel, 
250 feet long, may have a register tonnage of 700, and another 
of identical proportions may have a register tonnage of only 300, 
and yet both vessels may have equal displacements. Thus we 
gather that register tonnage gives no criterion of comparison 
between one vessel and another as to their dimensions, displace- 
ments, or deadweights. 

A glance at a Board of Trade Certificate of Survey for any 
vessel, or a Register of Shipping, shows three distinct tonnages, 
viz. : — Under-deck, gross, and register. One ton of under-deck, or 
gross tonnage, is equal to 100 cubic feet of capacity, so that these 
tonnages may convey some idea of the entire internal capacity 
of a vessel. Register tonnage, however, is a number having no 
dependence upon the internal capacity as a whole, as already 
stated, but is modified by the arrangement of the vessel, as 
affected by the space occupied by the propelling machinery and 
the crew, as well as other deductions allowed under the Merchant 
Shipping Act of 1894. 

Under-deck tonnage is the total tonnage up to the tonnage 
deck, and is the first part of the vessel measured for tonnage. 

Note. — The tonnage deck is the upper deck in all ships which have less 
than three decks, and the second deck from below in all other ships. 



240 



KNOW YOUft OWN SHIP. 



Under-deck tonnage is measured as follows : — 

If the vessel is constructed with ordinary floors, the depth at any 
part of the length of the vessel to the tonnage deck is measured 
from the top of the floors, afterwards deducting the average thickness 
of the ceiling, which is generally about 2 J inches, to one-third of the 
camber of the beam, down at the centre of the beam (see fig. 132). 

Should the vessel be built with a double bottom, the depth is 
taken from the height previously described (fig. 133) down to the 
plating forming the top of the double bottom where no ceiling 
is laid ; or, where there is ceiling, the average thickness (usually 




=1 



BREADJTHS _| 





Figs. 132, 133. — Under-Deck Tonnage ; Breadth and Depth. 

about 2| inches) is deducted from this depth — no allowance what- 
ever being made for grounds fitted between the tank top plating 
and the coiling. 

Where a vessel is constructed with ordinary floors at one part 
of her length, and a double bottom at another, the tonnage in the 
range of each part is computed separately, and the depths in each 
part are measured as just described for vessels with ordinary floors 
and double bottoms. 

The tonnage measurements for breadths are taken from the 
inside of the sparring in the hold, 2J inches being about the 
usual thickness. Sometimes, instead of wood sparring, half 
round iron is riveted to the reverse frames, especially in colliers. 
In this case the breadths are taken from the half round iron, 
side to side. Where neither sparring nor half roimd iron is 
adopted, the breadths are taken to the reversed frames, or to the 
inside of the framing. 

The length for underKieck tonnage is measured from the points 
at the extreme ends of the vessel where the inside lines of the 
sparring unite, or in the case where no sparring of any sort is 
fitted, to the points, where lines forming the inside of the framing 
imitc (fig. 134). 

The Board of Trade Surveyor then measures the inside of the 



TONNAGE. 



241 



vessel to the positions indicated, and by means of Simpson's 
Rules the cubic capacity in feet is found. If anything, this 
method of finding the cubic contents by these rules, gives the 
capacity rather under the actual, so that the diflFerence is slightly 
in favour of the shipowner. In the case of vessels of the raised 
quarter-deck type, the tonnage deck is the main deck, and where 





_ _^ LENGTH FO R TO NNAGE 




Fig. 134. — Length foe Undee-Deck Tonnage. 

the main deck stops, and the raised quarter deck begins, the line 
of the main deck is taken as the tonnage deck, as shown in 
fig. 135, and the capacity of the raised quarter deck is computed 
separately. 

Gross Tonnage comprises the under-deck tonnage, together 
with all enclosed erections in the form of poops, bridges, fore- 







TONNAG& DECK 




Fig. 135.— Tonnage Deck. 

castles, spar decks, awning decks, raised quarter decks, deck 
houses, engine and boiler casings,* etc. The chief exception to 
this rule is that the crew's galley, crew's w.c.'s, and companions 
are usually omitted in the calculations for tonnage. 

By enclosed erections is meant spaces closed in on all sides ; 
for example, poops with closed fronts of wood or iron, bridges 
with closed ends, and forecastles with closed ends. Open-ended 

* Engine and boiler casings form part of the gross tonnage, only, when, 
under paragraph 78 of the Merchant Shipping Act of 1894, the owner desires 
these spaces included in the calculation of the actual engine room. 

Q 



242 KNOW TOUR OWN SHIP. 

poops, bridges, forecastles, or deck shelter, usiBd only for the 
protection of passengers from the sea and weather, are not 
included in the gross tonnage. Should, however, any houses 
or storerooms of any kind be constructed beneath an open- 
ended erection, they are reckoned in the gross tonnage. 

Kegister Tonnage is obtained from the gross tonnage after 
certain allowed deductions have been made, and as the various 
dues and charges are levied upon this tonnage, the nature of the 
deductions will form the subject of our next consideration. First 
of all, it must be remembered that no deduction for any space 
whatever is made, unless it be first included in the gross tonnage. 
The deductions allowed, and the conditions required to ensure 
the same, are as follows : — 

1. Crew Space, — This must be available for the proper accom- 
modation of the men who are to occupy it, protected from sea 
and weather, properly ventilated and lighted; must contain 
72 cubic feet and 12 square feet of floor room per man; must 
be occupied exclusively by the crew and their personal property 
in use during the voyage, and reasonable w.c.'s provided. 

2. Master's Accommodation, — This space must be used exclu- 
sively by him, and be reasonable in extent. 

3. Engineers' and Officers' Accommodation. — This includes 
berths, mess rooms, and reasonable w.c.'s used by them alone. 

Note. — A mess room, used by both the captain and the officers, is not 
deducted for register tonnage. 

4. W.GJs. — In passenger steamers one w.c. for fifty passengers, 
and not more than twelve w.c.'s altogether are allowed, but only 
when situated above the tonnage deck. 

5. Sail Room. — This refers to sailing ships only, and on 
condition that the room does not exceed 2J per cent, of gross 
tonnage. If it does exceed this percentage, 2^ per cent, only 
of the gross tonnage is allowed. 

6. Boatswain's Store. — 10 to 16 tons is about the usual allowance 
for the average cargo steamer, varying according to the size of the 
vessel. 

7. Wheel Room, etc. — Space occupied exclusively for the 
working of the helm, the capstan, the anchor gear, or for 
keeping charts, signals, and other instruments of navigation. 

8. Donkey boiler, when not connected with the engine room. 

9. Deck shelter for passengers, when used only for this purpose, 
and closed at the ends. A sketch of this space must be sub- 
mitted to the Board of Trade, in order to obtain the approval 
necessary for its exemption from the tonnage. 

10. Propelling Deduciion. — The propeUing space includes 



TONNAGE. 243 

engine and boiler rooms, tunnel, donkey boiler space, if con- 
nected with, and forming part of the main engine space, light, 
and air space. This last comprises all space over or about 
engines and boilers of reasonable extent, and used exclusively 
for the admission of light and air;* it must also be safe and 
seaworthy. Any such space admitting light and not air, or air 
and not light, will not be included in the deduction. No stores 
of any sort must be carried in the propelling space. Store rooms 
or bunkers at the sides of the engines or the boilers will be ex- 
cluded in making up this deduction. These restrictions being 
fully complied with, paddle steamers with a propelling space of 
from 20 to 30 per cent, of the gross tonnage will have an allow- 
ance for propelling space of 37 per cent, of the gross tonnage. 
Screw steamers with a propelling space of from 13 to 20 per cent, 
of the gross tonnage will have an allowance for propelling space 
of 32 per cent, of the gross tonnage. If the propelling space is 
less than 20 per cent, in paddle vessels, and 13 per cent, in screw 
vessels of the gross tonnage of the ship, the Board of Trade have 
the option of either estimating the deduction at 37 per cent, in 
the case of paddle vessels, and 32 per cent, in screw steamers of 
the gross tonnage, or, if they think fit, allowing in the case of 
paddle vessels, once and a-half the propelling space tonnage, and 
once and three-quarters the propelling space in screw vessels. 
The latter method is usually adopted. 

When, however, the propelling space amoimts to 30 per cent, 
or more of the gross tonnage in the case of paddle vessels, and 
20 per cent, or more of the gross tonnage in the case of screw 
steamers, the owner has the option »of having the deduction 
estimated according to the 37 or 32 per cent, respectively, or, if 
he desires, the deduction may be once and a-half the propelling 
space in paddle vessels, and once and three-fourths the propelling 
space in screw vessels. The question arises as to which of these 
methods is more advantageous to the shipowner. Let us see. 
Suppose a paddle vessel has a given gross tonnage of 100, and 
a propelling space of 30 J tons. If the 37 per cent, method is 
adopted, the deduction will be 37 tons. If the once and a-half 
method is chosen, the deduction will be 30J+15J = 45f, which 
is certainly preferable from an economical point of view to the 
37 tons deduction. Again, let the gross tonnage of a screw 
steamer be, say, 100, and the propelling space 20 J, which pro- 
portion is not at all uncommon in vessels of average speed. 
Choosing the deduction of one and three-fourths of the propelling 
space, since the propelling space is over the 20 per cent., the 

* Only light and air spaces above the upper deck are referred to here. (See 
also footnote on page 241.) 



244 KNOW TOUR OWN SHIP. 

actual deduction would be If of 20J = 35|, which again is con- 
siderably more preferable than 32 as a deduction, and thus when 
we include the other deductions already enumerated, crew space, 
etc., we can easily understand how, in some vessels of compara- 
tively large dimensions, with largo propelling space, the register 
tonnage is abnormally small. Take a fine high speed passenger 
paddle steamer with a gross tonnage of, say, 100, and a large 
propelling space (situated amidships, and occupying the bulkiest 
part of the vessel) of, say, 40 tons of actual cubic measurement. 
The deduction would be once and a-half of 40 = 60 for propelling 
space, which without the other deductions is more than one-half 
the gross tonnage. A similar screw steamer with a gross tonnage 
of, say, 100, and propelling space by actual measurement of 30 
tons would have a deduction of once and three-fourths of 30 = 62 J 
for propelling space alone, also more than one-half of the gross 
tonnage. These are by no means exaggerated examples. It 
should be noted, that the higher the actual propelling space 
tonnage is above the 30 per cent, of gross in paddle vessels, and 
20 per cent, of gross in screw vessels, the greater is the proportion 
of deduction. 

In the ordinary tramp type of cargo steamers of comparatively 
low speed, and where all available space is required for cargo and 
bunkers, in many cases it might be found unwise to endeavour to 
get a propelling space of 20 per cent, of the gross tonnage, as this 
would require a sacrifice of too much space, which might be better 
utilised for bunkers or cargo. In vessels of this type, to obtain 
the 20 per cent, generally implies that it is only done by fitting 
no side bunkers in engine or boiler space, or at most, small pockets. 
However, this is a point needing the careful consideration of the 
shipowner or designer of the vessel. 

From the study of these deductions, it is evident that the Board 
of Trade have given every encouragement to the providing of 
suitable accommodation, or at least, reasonable berthing for officers, 
and crew especially, for perhaps of all the comfortless and for- 
bidding liuman habitations, the forecastles of some vessels would 
claim a foremost place. We have also seen the advantage gained 
by providing, when practicable, spacious and well-ventilated engine 
and boiler rooms. 

Before giving a few examples of the tonnage of actual vessels, 
it may be well to point out one or two items from the Board of 
Trade Tonnage Rules, which might be misunderstood. 

In vessels constructed with double bottoms for water ballast, 
the measurement for tonnage is only taken from the inner bottom, 
plating (or ceiling), when the space between the inner and the 
outer bottom, of tofiatever depth, is certified by a Board of Trade 



TONNAGE. 245 

Surveyor to be not available for the carriage of cargo, stores, or 
fuel. 

Deep Water Ballast Tanks. — Should, however, a vessel be 
built with a raised platform in the bottom, or in other words, a 
deep tank, thereby making it possible for cargo, stores, or fuel 
being carried in this space, the depths for tonnage are taken down 
through the platform, or the deep tank, to the height of the 
ordinary floors, deducting the average thickness of ceiling (if 
any). 

Fore and after peak tanks, though constructed and intended 
only for water ballast, are included in the measurement for 
tonnage, unless, after submitting sketches to the Board of Trade 
showing the construction, means of entering, and position of the 
peak top plating in relation to the load waterline, exemption of 
these spaces from the gross tonnage be granted. 

Deck Cargo. — Ships engaged in the foreign trade, carrying 
deck cargoes in the form of timber, etc., in spaces not included in 
the measurement of the tonnage of the vessel, have the space 
occupied by such cargo measured when the vessel arrives in port, 
and the cubic capacity being computed, and divided by 100, gives 
the tonnage which is deemed register tonnage, and charged upon 
accordingly. Between the 31st of October and the 16th of April, 
vessels from any port out of the United Kingdom are not allowed 
to carry deck cargoes exceeding 3 feet in height above the deck, 
under penalty. 

Examples. — 

Example I. 

Steam screw collier, 228 feet long. Raised quarter-deck type. 

Gross Tonnage — 

Under-deck tonnage, 680 

Erections — 

Raised quarter deck, 60 

Poop, t . . 47 

Bridge 120 

Lamp room under open forecastle, 5 

Casings and deck houses on bridge,* .... 36 

Excess of hatches over J per cent, of gross tonnage, . 16 

Total 964 

Propelling space, 210 = 21 "7 per cent, of gross tonnage, therefore the If 
of actual propelling space is chosen. 

1} of 210 = 367-5. 

* It shotdd be understood that where the actual propelling space is over 
13 per cent, and considerably less than 20 per cent, of uie gross tonnage, it 



246 KNOW TOUR OWN SHIP. 

Had the propelling space been less than 20 per cent, of the 
gross tonnage the deduction would only have been 32 per cent. 
of the gross tonnage = 308*4, which makes a diflFerence in the 
ultimate register tonnage of 367*5 - 308*4 = 59*1. In tramp 
vessels of this type it is not very usual for the propelling space 
to exceed the 20 per cent, of gross tonnage. However, it will 
be seen how spacious light and air space in the casings above the 
tonnage deck will greatly assist towards this end. Sometimes 
boiler casings are made wide enough for unshipping the boilers 
without interfering with the deck. 

The deductions for the register tonnage in this vessel were as 
follows : — 

Propelling space, . . . 367*5 
Chart room, .... 5 
Bridge accommodation for officers, 54 
Crew space, .... 28 
Boatswain's store, . .10 



Total, . . 459*5 



Gross tonnage, . 964 
Total deductions, . 459*5 



Register tonnage, . 504*5 
EXAMPLB II. 

Passenger steamer, 200 feet long, with a combined poop and 
bridge, and a topgallant forecastle. 

In vessels of this type, where a high speed is required, the 
propelling space usually exceeds the 20 per cent, of gross tonnage 
considerably, as seen by the following figures : — 

Under-deck tonnage, .... 530 
Poop, bridge, and forecastle, . 285 

Deck houses and casings, ... 40 

Gross tonnage, . . 855 

Propelling space measured 235 tons = 27 per cent, of gross 
tonnage. 

The allowance, therefore, is If of 235 = 411 (32 per cent, of 
gross = 273*6). 

is unnecessary to include the light and air casings above the upper deck in 
the tonnage. Sometimes where the actual propelling space is alightly less 
than 13 per cent, of the gross the addition of the light and air casings or part 
of these spaces may secure this percentage. 



TONNAGE. 247 



Deductions for register tonnage are as follows : — 

Propelling space, . . . .411 

Crew, 40 

Passengers' w.c.'s, . . . . 4 
Master's accommodation and chart room, 7 
Boatswain's store, .... 10 

Total. ... 472 

Gross tonnage, . 855 
Total deduction, . 472 

Register tonnage, . 383 

Example III. 

Sailing-ship, 320 feet long, with a poop and a topgallant 
forecastle. 

Under-deck tonnage, .... 2900 

Poop 110-5 

Forecastle, 20*4 

Houses on deck, . . . . 8'0 

Gross tonnage, . . 3038*9 



HA^ 



Deductions for register tonnage are as follows : — 

Crew space, 115'9 

Boatswain's store, .... 15 

Chart house 4 

Sail room, 20 

Total, .... 154-9 

Gross tonnage, . 3038 '9 
Total deduction, . 154*9 

Register tonnage, 2884 

In sailing-vessels we always find the gross tonnage large as 
compared with steamers. This is accounted for by the fact, 
that there being no engines and boilers, and, therefore, no 
propelling space deduction, the entire hold space is at the 
disposal of cargo. 

Suez Canal Tonnage. — For ships intended to navigate the 
Suez Canal, a special tonnage certificate is required, since the 
method of computing the nett register tonnage differs in a few 
of its details from the ordinary system. 

The extract given on the next page is taken from the Regulations 



248 - KNOW TOUB OWN SHIP. 

for the Namgation of the Canal, and may be of interest to those 
unacquainted with the canal requirements : — 

" When a ship intending to proceed through the canal shall have dropped 
anchor either at Port Said or Port Thewfik, the captain must enter his snip 
at the Transit Office and pay all dues for passage, and when there is occasion, 
for pilotage, towing, and berthing ; a receipt for the same shall be delivered 
to him, which will serve as a voucher whenever required. 

" The following information must be handed in by the captain : — 

** Name and nationality of the ship, to be identified by exnibiting the ship's 
papers respective thereto. 

** Name of the captain. 

" Names of the owners and charterers. 

**Port of sailing. 

" Port of destination. 

** Draft of water. 

' ' Number of passengers as shown by the passage list. Statement of the crew 
as shown by the muster roll and its schedules. (Sailors occasionally taken on 
board of vessels passing through the Suez Canal are not considered as forming 
part of the crew, and are taxed in conformity with the present regulations. ) 

'* Capacity of the ship according to the legal measurement ascertained by 
producing the special canal certificate, or the ship's official papers established 
in conformity with the Rules of the International Tonnage Commission, 
assembled at Constantinople, in 1873." 

Upon arrival at the canal the captain of every vessel receives a copy of the 
ItegulatioTis, 

The under-deck tonnage is measured, as shown in figs. 132, 
133, 134, in the case of vessels constructed throughout with 
ordinary floors or a cellular double bottom with horizontal top. 
In vessels with a break or breaks or other irregularities in the 
construction of the bottom, a slight difference arises owing to the 
method of computation. Vessels with cellular double bottoms, 
with the tank top rising from the fore and aft middle line to the 
bilges, average about 3*5 per cent, less than the British for 
imder-deck tonnage, owing also to a modification in the mode of 
computation. In vessels built with Macintyre tanks, the depths 
for tonnage are taken to the top of the inner bottom plating, as 
in British. Under no circumstances are peak or any other tanks 
exempted from the under-deck tonnage. 

The gross tonnage includes, in addition to the under-deck 
tonnage, every permanently-covered and closed-in space on or 
above the tonnage deck without any exception. Such a space 
as a shelter under a shade deck, open at the sides and supported 
by means of stanchions, would, therefore, be excluded from the 
gross tonnage. 

The deductions for nett register tonnage are as follows : — 

1. Propelling Space, 

The owner has the option of either of the following methods : — 
(a) The deduction may be one and three-fourths of the actual engine room 
as measured for screw steamers, and one and a-half for paddle vessels ; o^, 



TOKNAQfi. 24& 

(b) The actual measurement of the engine room, together with the actual 
measurement of the permanent bunkers. 

Note 1. — Bunkers which are portable, or from which coal cannot be directly 
trimmed into the engine room or stokehole, or into which any access can 
be obtained otherwise than through the ordinary coal shoots on deck, and 
from doors opening into the engine room or stokehole, are not included in 
the measurement in paragraph {b). In no case, except in that of tugs, is 
the actual engine room allowance to exceed 60 per cent, of the gross tonnage 
of the ship. 

Note 2. — Light and air spaces over the engines and boilers and above the 
uppermost deck do not form a part of the actual engine room, except when 
situated in a permanently-enclosed bridge space, poop, or other erection. 

2. Crew spaces, exclusively and entirely occupied by the crew 
and ship's officers, with the exception of the master, stewards, 
cooks, passengers, servants, purser, clerk, etc., in short, only 
such spaces are deducted as are occupied and used by those 
persons engaged in the navigation and propulsion of the vessel, 
with the exception of the doctor's cabin, when he is actually on 
board and occupying such space. Also the covered and closed-in 
spaces above the uppermost deck employed for working the ship. 

Not more than 4 tons are allowed for an officers' and engineers' mess room. 

For a second mess room for boatswain, carpenter, etc., not more than 2} 
tons are allowed. 

Should passengers be carried and no eating room be provided for them, 
no deduction whatever is allowed for officers' and engineers' mess room. 

When no passengers are carried, a bathroom, used entirely for the officers 
and engineers, is reckoned as a deduction, and even when passengers are 
on board, if there be more than one permanent bathroom, one of such spaces 
is subject to deduction, being considered as specially for the use of officers 
and engineers. 

Not more than 2 tons are allowed for a bathroom. 

3. TT.C's, exclusively for the use of the crew. 

4. Wheel house, chart hovse, winch hcnise, look-out house. 

Should the captain be lodged in the chart room, an allowance of 3 tons is 
made for the space occupied by charts. 

5. Cooking houses, used only for the crew. Passengers' galleys 
are therefore not deducted from the gross tonnage. 

6. A donkey boiler house in a closed space on the upper deck. 
Should, however, the donkey boiler be used for hoisting cargo 
no deduction is allowed. 

In no case is the sum total of these deductions, with the excep- 
tion of propelling space, to exceed 5 per cent, of the gross tonnage 
of the ship. 

No deduction is made for spaces used, or which may possibly 
be used, for passengers' accommodation ; captain or passengers' 
w.c.'s or lavatories, luggage storerooms, boatswain's store, or 
sailroom. 



250 



KNOW tOUft OWN sHir. 



In no case is any space to be deducted from the tonnage, which 
is not first included in the gross tonnage. 



YACHTS. 

Yachts are measured for tonnage in exactly the same manner 
as ordinary merchant vessels, the same deductions being allowed 
for register tonnage. 

For example, take a steam yacht 180 feet long. The gross 
tonnage would be comprised as follows : 

Under-deck tonnage, . . 520*5 
Deck houses, ... 10 
Monkey forecastle, . . 6*1 



Total, . . 536*6 






Deductions for register tonnage : 






Propelling space, . . . 220*6 
Crew space, . . . . 49'5 
Master's room, . . . 3*5 


■ 




Chart room, . . . 3*0 






Boatswain's store, . . 3*2 






Total, . . 279-8 






Gross tonnage, . 
Total deduction, 

Register tonnage, 


. 536*6 
. 279*8 




. 266*8 



Measurement of Yachts for " Royal Thames " Yacht Club, 

Measure the length of the yacht in a straight line at the deck 
from the fore part of the stem to the after part of the stem 
post. From this length deduct the extreme breadth. If the 
vessel be iron or steel, this breadth is taken over the plating, 
and if composite or wood, over the planking. The remainder is 
the length for tonnage. If there be any projection of the stem 
or stern posts beyond this length, such projection must be added 
to the length already mentioned for tonnage purposes. Multiply 
the tonnage length by the extreme breadth, then that product 
by half the extreme breadth, and divide the result by 94. The 
quotient will be the tonnage. 

Example. — Steel yacht 200 feet extreme length over stem and stem posts 

28 feet extreme breadth. 

200 - 28 = 172 feet, length for tonnage. 
172 X 28 X 14 



94 



= 7l7ff tonnage Thames measurement. 



PBfiEfiOAHt). 2^1 



CHAPTER IX. 
FREEBOARD. 

Contents. — Definition — Method of Computing Freeboard — Type of Vessel 
— Nature of Deductions, and Additions to Freeboard — Examples of 
Estimating Freeboard for Different Types of Vessels. 

Definition. — B y the te rF> T^'^pphnr^vt^ in mpgyit the ^?^g^^ of. the 
side of ^ «bifi^J;>ov^ the waterline . at ^ the middle of. her length, 
measured from the top of the deck- at tha fiida. Should a wooden 
deck be laid, it is taken from the top of the wooden deck. In 
fig. 3, X shows the amoujit of freeboard, which, as will bo ob- 
served, is 2 feet. 

Buoyancy, Structural Strength, Stability, and Freeboard are 
subjects closely related to each other ; indeed, the latter depends 
almost entirely upon the other three. Hence the necessity, in 
order to deal intelligently with freeboard, that the reader should 
make himself acquainted with the contents of Chapters III. to 
VI. inclusive. 

Freeboard is given to a vessel as a margin for safety. For 
instance, it would be possible for a ship to float with her deck 
edge level with the water; but in such a condition, having no 
reserve bouyancy she possesses no rising force, and would, there- 
fore, be submerged beneath every wave, to say nothing, more- 
over, of the possible effect of such a condition upon her stability. 

The amount of freeboard for a particular vessel is modified by 
the type, structural strength, erections on deck, sheer, camber, 
etc. It must be borne in mind, however, as previously shown, 
that such freeboard can only fully perform its chief function, 
and be a real resource of safety, after a proper adjustment of 
cargo has been carried out in the operation of loading. The 
effect of freeboard on stability has already been dealt with in 
Chapter VI. 

Flush-decked steamers, other than spar- and awning-decked, 
and equal in structural strength to 100 Al at Lloyd's, or equi- 
valent strength at Bureau Veritas, or the British Corporation or 
other classifying association, require from about 20 per cent, to 
35 per cent, reserve buoyancy, according to their dimensions. 



252 



KNOW YOUB OWN SHIP. 



This enables a vessel of suitable proportions to carry with safety 
a deadweight for which her structural strength is adapted, and 
to endure without damage the severe strains incurred when 
among waves, already discussed in Chapter IV. 

Therefore, all vessels below the standard of the one-, two-, and 
three-deck type in structural strength, are compelled to carry a 
smaller deadweight in proportion to their dimensions, with the 
result that they have increased reserve buoyancy, and, conse- 
quently, increased freeboard. Hence the spar-decked vessel, as 
will be seen further on, requires a larger percentage of reserve 
buoyancy than the one-, two-, and three-deck vessel; and the 
awning-decked a larger percentage of total reserve buoyancy 



Scale of Cubic Feet Capacity. 



4COO 




Fig. 136.— Cukve of Cubic Feet of Capacity. 



than the spar-decked one, which results in both cases in 
providing increased freeboard. Sailing-vessels require rather 
more reserve buoyancy than steamers. 

An examination of the Board of Trade Tables for such vessels 
shows that this is the standard worked upon, the aim being to 
give a freeboard such as will secure the stipulated amount of 
reserve buoyancy, and thus give to vessels of suitable dimen- 
sions sufficient strength for the total weight, including cargo, to 
be carried, and the rising power and stability (when properly 
loaded) requisite, when exposed to heavy weather, to ensure 
safety. 

Now, suppose we had a flush-decked vessel, classed 100 Al at 
Lloyd's, to which we wished to assign a freeboard producing 20 



FBBBBOABD. 253 

per cent, reserve buoyancy. To find this accurately, it would 
be necessary to construct a curve of capacity, identical in its 
construction with a displacement curve, except that it shows 
the whole external volume up to the deck, and instead of a scale 
of tons at the top, the scale would represent cubic feet of 
capacity. 

Fig. 136 represents such a curve for a vessel 16 feet depth 
moulded. It, therefore, comprises the total buoyancy of the 
vessel up to the deck. This is found to be, say, 20,000 cubic 
feet total buoyancy. 20 per cent, of 20,000 = 4000 cubic feet 
to be left above the load waterline= reserve buoyancy. 

20,000-4000 = 16,000 cubic feet from the keel to the load 
waterline. This equals the vessel's load displacement, which 
gives by the scale a draught of 14 feet, and a freeboard of 2 feet. 

But, as is evident, this method entails considerable labour, 
and would necessitate a copy of the vessel's lines being supplied 
to the Board of Trade or Registration Society fixing the free- 
board, and, therefore, in order to obviate this, another method 
is adopted, which, though not strictly accurate, is sufl&ciently 
correct for all practical and working purposes. 

In the last chapter we saw how the Board of Trade Surveyor 
measured the vessel for tonnage, and the results obtained provide 
one of the principal factors in estimating the requisite freeboard. 

In Chapter I. it was shown how coeflficients of fineness of 
displacement were obtained, and in a similar manner a coefficient 
of fineness is obtained from the tonnage under the upper deck, 
and this, combined with the dimensions of the ship, as will be 
explained, serves the same practical purpose, in referring to the 
Freeboard Tables, as would the actual volume of the ship. 

The coefficient of fineness is ascertained as follows : — For one-, 
two-, and three-deck, and spar-decked vessels, divide 100 times 
the total tonnage (1 ton measurement being 100 cubic feet) 
below the upper deck (exclusive of any deductions) by the 
product of the extreme length over the stem and the stem 
posts on the load waterline, the extreme breadth over the 
plating, and the depth of the hold.* In awning-decked vessels, 
divide the tonnage to the main deck, by the product of the 
length, the breadth, and the depth of the hold to the main 
deck. In the case of vessels built with cellular double bottoms, 
a modification or correction has to be made in estimating the 
coefficient. It should, however, be remembered that the co- 
efficient obtained is that of a vessel built with ordinary floors. 

* The depth of hold used in ascertaining the coefficient of fineness is 
taken to the top of the ceiling in iron and steel sailing-vessels, and to the 
top of the floors in steamers. 



254 KNOW YOUB OWN SHIP. 

As an example, the tonnage under the upper deck of a certain 
vessel is 78*4 ; 

78-4 X 100 = 7840 cubic feet. The length is 100 feet, 

The extreme breadth is 16 feet. 
The depth of hold is 7 feet, 
100 X 16 X 7 = 11,200. 

^^^^ = 0-7 Coefficient of fineness. 



11,200 



and this coefficient is that used, in conjunction with the moulded 
depth, to find the freeboard for this particular vessel from the 
Tables. 

The greater the depth of the vessel, the greater the freeboard. 
The depth from which the freeboard, as ascertained by the 
Tables, is measured, is the moulded depth, which is taken from 
the top of the keel to the top of the upper deck beam at the 
side, at the middle of the length. When a wooden deck of 
extra thickness is fitted, the excess of thickness is added to 
the moulded depth, and the freeboard taken upon this new 
depth. Now, as wo have already pointed out, the structural 
strength is a most important consideration in determining free- 
board, the strongest ship with suitable proportions having the 
least freeboard. The strongest vessel is the one-, two-, and three- 
deck type, classed 100 Al at Lloyd's, or any other vessel, classed 
or unclassed, but of equivalent strength. Next, we have the 
spar-decked, and, lastly, the awning-decked vessel. 

In assigning freeboard, the term "spar-decked vessel" applies 
to all vessels equal to, or in excess of, the strength of Lloyd's 
Spar-deck Rule, but do not reach the structural standard of 
the three-deck requirements. The freeboard, therefore, depends 
upon their strength. The standard height for a spar-deck is 
7 feet ; therefore, since the freeboard is measured from the 
spar-deck, it will be increased if the 'tween deck height is 
more, and decreased if it is less than 7 feet. 

In like manner, an awning-decked vessel is one equal to, or 
exceeding Lloyd's structural requirements for awning-decked 
vessels, but which does not reach the standard for the spar-deck 
type. In this case also, the freeboard varies with the strength. 
When the strength of the superstructure above the main deck 
is less than is required by Lloyd's 100 Al Awning-deck Rule, 
the freeboard is increased. The awning deck may, therefore, be 
classed as simply an erection above the main deck, and since the, 
freeboard is measured from the main deck, no modification is 
necessary in respect to the height of the awning deck above the 
main deck. The freeboard of awning-decked vessels classed 
100 Al at Lloyd's is approximately one-twelfth the moulded 



FBEEBOABD. 255 

depth of the vessel less than would have been required had it 
been built to the three-deck Rule, and flush decked. 

No account is taken of erections above the awning deck of 
vessels of this type. This also applies to spar-deck vessels with 
but one exception. Since the longitudinal strains of vessels are 
greatest in the region of amidships, it follows that any efficient 
erection over this part of the length must add greatly to the 
Strength. Such an erection receives full credit in assigning 
freeboard in the three-decked heavy deadweight carrier. A 
similar erection in the form of an efficient bridge on a spar- 
decked vessel, extending over and protecting the engine and 
boiler openings for at least two-fifths of the vessel's length, also 
receives recognition on account of its addition to strength and 
protection, though not in so great proportion £is in the three- 
decked type. Thus such an erection on a spar-decked vessel of 
20 feet moulded depth to main deck, merits a reduction of 
3 inches on the freeboard. 

For the sake of comparison, let us see the diflferences of free- 
board in a vessel of each of these types — three-decked, spar- 
decked, and awning-decked, classed 100 Al at Lloyd's. Let the 
length in each case be, say, 300 feet, the coefficient of fineness '7, 
and the depth to main, spar, and awning deck 25 feet, the spar 
and awning deck each being 7 feet above the main deck. 



The vessel of the first type would have a freeboard of 5 feet ' 

Oi inches. 
The spar-decked would have a freeboard of 6 feet 2 inches. 
The awning-decked would have a freeboard of 8 feet 7 J inches. > 



r 



For summer 
voyages. 



But even after the coefficient of fineness is found, there are 
certain modifications to be carried out before the exact freeboard 
is arrived at, and these modifications will next be dealt with. 

Let it be understood that only vessels equal in strength to 
Lloyd's 100 Al will be considered. Vessels below this standard 
have increased freeboard : — 

1. In spar-decked vessels, having iron-spar decks, and in 
awning-decked vessels having iron main decks, the freeboard 
required by the tables should be measured as if those decks were 
wood-covered. Also, in vessels where j^^ths, or more, of the main 
deck is covered by substantial enclosed erections, the freeboard 
found from the tables should be measured amidships from a 
wood deck, whether the deck be of wood or of iron. In apply- 
ing this principle to vessels having shorter lengths of substantial 
enclosed erections, the reduction in freeboard, in consideration 
of its being measured from the iron deck, is to be regulated in 
proportion to the length of the deck covered by such erectio 



256 KNOW YOUR OWN SHIP. 

Thus, in a vessel having erections covering ^^ths of the length, the 
reduction is ^^^ths of 3^ inches (the thickness of the wood deck), 
or 2 inches. 

2. In flush-deck vessels of the one-, two-, and three-deck type, 
and those of the same type with erections extending over less 
than ^ths of the length, having iron upper decks not sheathed 
with wood, the usual thickness of a wood deck is deducted from 
the moulded depth of the vessel, and the freeboard taken from 
the column in the tables corresponding with the diminished 
depth. Thus, a vessel of this type with 19 feet 10 inches 
moulded depth, with no laid wood deck, would be reckoned 
as 19 feet 6 inches depth in the tables. Taking the coefficient 
of fineness of this vessel at '7, referring to the freeboard tables, 
the freeboard at 19 feet 10 inches depth would have been 3 feet 
7^ inches, where, owing to the reduction of the depth to 19 feet 
6 inches, the freeboard is 3 feet 6J inches. When the erections 
in vessels of this type cover more than ^ths, and less than 
^ths of the length, the correction for the wood deck is made 
as explained towards the end of the previous paragraph. 

3. Correction for Length, — The freeboard tables show that in 
addition to the coefficient given with every depth, a fixed length 
is assigned. For example, a vessel with a coefficient of 0*7, and 
a depth of 16 feet, a length of 192 feet is assigned, but if the 
length of our vessel with the same coefficient and depth be, say, 
212 feet, a correction must be made for the additional 20 feet 
of length. Wherever the standard length is exceeded, the free- 
board is increased, and wherever it is less, the freeboard is 
diminished. The greater the proportion of length to depth, the 
greater the freeboard. The correction varies from about '7 to 
1*7 inches for a change of 10 feet in length. In the case before 
us, the correction is 1 inch per 10 feet, and thus for 20 feet it is 
2 inches, which has to be added to the specified freeboard in the 
table. Had the vessel been 10 feet less than 192, the freeboard 
would have been reduced by 1 inch. The reason for this is 
easily understood when we remember that the vessel with 
greatest depth to length is the one most capable of resisting 
longitudinal bending, and therefore best adapted to carry the 
most deadweight. Where, however, steam-vessels with top- 
gallant forecastles, having long poops or raised quarter decks 
connected with bridge houses, the whole extending over -j^ths, 
or more, of the length of the vessel, the correction for excess 
of length should be half that specified in the tables ; so that if 
the vessel we have taken as an example complied with these 
conditions, the freeboard would only have been increased by 
1 inch, simply because with so great a length of substantial 



PRBBBOARD. 257 

erections, the vessel has practically been increased in depth, and 
consequently the proportion of depth to length is decreased. 

The correction for length in spar-decked vessels varies from 
about '9 to 1*5 inches per 10 feet, and for awning-decked vessels 
from about '5 to '8 of an inch. 

4. Sheer. — The Board of Trade Tables specify a mean sheer 
for all types of vessels. Mean sheer is the sum of the sheers 
at the ends of the vessel, or at whatever part of the length it 
is specified, divided by 2 (see fig. 18). 

Any increase in the mean sheer means an increase in the 
reserve buoyancy, and exactly where it is much needed — viz., 
at the ends, giving additional rising power when the ship dips 
into the trough of a sea, not to mention the increase of free- 
board. This excess of buoyancy is recognised by the Board of 
Trade, and a deduction allowed in the freeboard according to 
the amount of the excess of sheer. 

For all flush-decked vessels, the mean sheer is found by 
dividing the length by 10, and adding 10 to the result Thus 

a vessel 300 feet long will have a mean sheer of — — + 10 = 40 

inches. 

Flush-decked vessels of the one-, two-, and three-decked type, 
with or without a short poop, a topgallant forecastle, and a 
bridge house completely closed in at the ends, or a long poop, 
or a raised quarter deck connected with an efficiently closed-in 
bridge house, where the sheer is greater than in the Table, and 
is of a gradual character, the reduction in freeboard is found by 
dividing the difference between the actual sheer and the mean 
sheer provided for in the Table, by 4. For example, a vessel 300 
feet long, with a mean sheer of 46 inches, has a reduction in the 

freeboard of ~ — = — = H inches. No allowance is given 

to spar- and awning-decked vessels for excess of sheer; but in 
any of these types, where the actual mean sheer is less than the 
mean sheer by the rule, the difference divided by 4 gives the 
increase of freeboard required for reduced reserved buoyancy. 

Line 1 in the Table (p. 258) is for vessels having short poops or 
forecastles only, or when, in addition, there is a bridge house, 
with alleyways open at one or both ends. In these vessels the 
important point is not the amount of sheer at the ends of the 
vessel, for great additional buoyancy is given there already by 
the erections, but over the length uncovered by substantial 
erections. Therefore, in this particular case, the sheer is 
measured at one-eighth the vessel's length from stem and stem. 
One-fourth the difference between the sheer and the actual mean 



258 



KNOW YOUR OWN SHIP. 



is approximately the amount of increase or decrease of freeboard, 
as the case may be. 

Length oyer which Sheeb is Measured. 





100 


150 


200 


260 


300 


350 


400 


Mean Sheer in Inches over the Length specified. 


No. 1, 

No. 2, 


14 
144 


18 
18i 


22 
23 


26 

27 


30 
31 


34 
35i 


38 
40 



Line 2 in the Table is for vessels having short forecastles only, 
and in this case the sheer is measured at points (1) one-eighth 
from the stem, and (2), at the stern post, and correction for 
additional sheer is made as in the previous case. 

Note, — In flush-decked vessels, and in vessels having short poops and 
forecastles, the excess of sheer for which an allowance is made is not more 
than oue-half the total standard mean sheer for the size of the ship. 

5. Round of Beam, — Th6 stipulated round of midship beam is 
a quarter of an inch for every foot of the length of the mid- 
ship beam. Here, again, any excess in the round of beam means 
an increase of reserve buoyancy, and an allowance is made in the 
freeboard. When the r'oimd of beam in flush-decked vessels is 
greater or less than that given by the Kule, divide the diflference 
in inches by 2, and diminish or increase the freeboard accordingly 
by this amount. 

Example. — The beam of a vessel is 40 feet, and the round of beam as 
measured is 12 inches. This is 2 inches more than is required by the Kale, 
therefore ^ = 1 = amount of decrease of freeboard. Where the deck is 
partially covered with erections, the amount of the allowance for round of 
beam depends upon the extent of the upper deck uncovered. 

This rule for round of beam does not apply to spar- and awnmg- 
decked vessels. 

6. Corrections for Erections on Deck, — By erections on deck 
is meant all closed-in or partially closed-in structures erected 
above the upper deck of vessels built to the one-, two-, or three- 
deck rule, — for example, bridges, poops, forecastle, raised quarter 
decks, partial awning decks, etc., and also strong bridges in spar- 
decked vessels covering the engine and boiler openings if such 
erections extend over at least two-fifths of the vessel's length. 
Now, erections such as those enumerated add greatly, according 
to their proportions, to the reserve buoyancy, and, as in the case 
of sheer and camber, the merits of the values of these erections 



FBBBBOABD. 259 

and additions to the reserve buoyancy and structural strength, 
and the protection afforded to vulnerable localities such as deck 
openings, are fully considered by the Board of Trade, and de- 
ductions in the freeboard allowed accordingly. In assigning 
allowances for erections, the complete awning deck is the standard 
worked from. 

As has already been pointed out, in taking out the freeboard 
for a vessel with an aw^ning deck, the coefficient of fineness and 
the depth are both taken to the main deck, and not to the awning 
deck, and the freeboard is assigned and measured down from the 
main deck. The awning deck thus comes to be what might be 
termed a complete erection, extending all fore and aft, and 
covering the main deck. All other erections partially covering 
the vessel have their deductions on the freeboard made as a frac- 
tional part of a percentage of the allowance for a complete awning 
deck. The reader will easily see that a complete erection such as 
an awning deck is always better than a partial one, comparing 
length for length ; for instance, an erection covering three- 
fourths of the vessel's length cannot be taken on equal merits 
with three-fourths of the awning deck, since it is evident that 
a well has been created on the weather deck in some part of the 
vessel's length, forming a break in the longitudinal strength of 
greater or less importance, and a means thus provided, to some 
extent, for lodging seas on board, or the possibility created of 
bulkheads being damaged, etc., therefore, three-fourths' erections 
do not receive the same credit as three-fourths of the awning 
deck, but a less fractional part. Again, the allowance varies 
with the nature of the erections. This we shall endeavour to 
show by arranging the erections according to their respective 
values. 

Taking a vessel 204 feet long, and, therefore, with an awning- 
deck erection of the same length, we shall see what credit is 
given, in assigning the freeboard according to the Board of Trade 
Tables of Freeboard, for the various kinds of erections in 
comparison with the allowance for the complete awning-deck 
erection. This, it is hoped, will better enable the reader to 
grasp the comparative values of the erections. 

Let the moulded depth of the vessel be 17 feet, and the coefficient of 
fineness '7. 

The freeboard, had the vessel been flush -decked, to the two-deck rule would 
have been 2 feet 10^ inches. 

The freeboard, had the vessel been awning-decked, would have been 1 foot 
4 inches. 

2 feet lOJ inches - 1 foot 4 inches = 1 foot 6} inches = 18} inches, 

this difference being the allowance for the complete awning-deck erection. 



260 KNOW YOUR OWN SHIP. 

Note, — For a raised quarter deck, 4 feet high, and connected with a bridge 
house, covering the engine and boiler openings with an efficient bulkhead at 
the fore end, the allowance is made as though it were a part of the actual 
bridge, and equal in height. A decrease is made in the deduction, if the 
raised quarter deck extends over the engine and boiler openings, or if it is 
less than 4 feet high. 

The deductions for erections are as follows : — 

1. When the combined length of poop, or raised quarter deck, 
connected with a bridge house covering in the engine and boiler 
openings, and with an efficient bulkhead at the fore end, and top- 
gallant forecastle is — 

(a) y\ or '9 of the length of the vessel, 

the deduction is *85 of the allowance for a complete awning deck. 

Freeboard is ^Vtj" of 18^ inches = 15J inches. 
(&) Y% or "8 of the length of the vessel, 

the deduction is 75 of the allowance for awning deck. Freeboard is 

yVv of ^^h inches = 13J inches, 
(f) /^ or '7 of the length of the vessel, 

the deduction is '63 of the allowance for awning deck. Freeboard is 

iVtf of 18^ inches = 11| inches. 
(d) T*iT or *6 of the length of the vessel, 

the deduction is '5 of the allowance for awning deck. Freeboard is 

^ji of 18| inches=9J inches. 

These comprising the maximum reductions, it is essential that 
the erections be of a most substantial character, the deck openings 
effectually protected, the crew berthed in the bridge house, or 
with satisfactory arrangements to enable them to get backward 
and forward to their quarters, and sufficient clearing ports in the 
bulwarks to speedily clear the deck of water. Vessels of this 
type having no topgallant forecastle are allowed a less deduction 
in the amount of freeboard than would otherwise be given for the 
same length of erections. And if the bridge be a short one, in 
front of, and only partially covering the engine and boiler open- 
ings, again a less deduction is made. No allowance is granted for 
a monkey forecastle which is less in height than the main or 
topgallant rail. 

Note 1. — A special allowance is made on the freeboard of vessels of the 
foregoing or well-decked type when their erections extend over -^ of their 
length, when their bridge bulkheads are specially strengthened, and when 
the area of their water clearing ports in the bulwarks is at least 25 per cent, 
in excess of the rule requirements. Such additional allowance must not 
exceed 2 inches. 

Note 2. — Special reductions in the freeboard may be obtained in strong 
well-decked vessels of the modern type, having erections covering at least 
Y^^ths of the length of the ship, the bridge house alone covering at least 
^\ths of the length when extra strength is introduced, as given in section 44, 
Lloyd's Rules for 1889, for iron and steel vessels. But, in no case most the 
freeboards assigned to these vessels be less than would be assigned for a com- 
plete awning deck. 



FRBBBOARD. 261 

2. In vessels with topgallant forecastles, short poops, and 
bridge houses covering engines and boilers in steamers, with 
efficient iron bulkheads at their ends, when the combined length 
of erections is — 

(a) -^ or '5 of the length of the vessel, 

the deduction is '4 of the allowance for awning deck. Freeboard is 

f of 18^ inches = 7i inches. 
W Tn or '4 of the length of the vessel, 

the deduction is *33 of the allowance for awning deck. Freeboard is 

^ of 18^ inches = 6 J inches. 

3. In vessels with topgallant forecastles and bridge houses only, 
covering engines and boilers in steamers, with efficient iron bulk- 
heads at the ends, when the combined length of erections is — 

(a) -^ or "4 of the length of the vessel, 

the deduction is '3 of the allowance for awning deck. Freeboard is 

■^jj of 18^ inches = 5| inches. 
{b) y% or '3 of the length of the vessel, 

the deduction is '26 of the allowance for awning deck. Freeboard is 

J of 18^ inches = 4f inches. 

4. In vessels with only topgallant forecastles and poops, the 
latter with an efficient bulkhead at the fore end, when the com- 
bined length of erections is — 

(a) f of the length of the vessel, 

the deduction is ^ of the freeboard for the vessel flush decked. Free 

board is ^i^^ of 34^ inches = 3^ inches. 
{b) I of the length of the vessel, 

the deduction is y^^ of the freeboard for the vessel flush decked. 

Freeboard is ^hs of 34^ inches = 2J inches. 

5. In vessels with topgallant forecastles only, the deduction 
in freeboard is only one-half that prescribed in the previous para- 
graph. Thus, were the erection ^ of the length of the vessel, 
the deduction would be y^ of freeboard for the vessel flush 
decked = If inches. 

6. In vessels with poops only, the allowance is one-half that 
for the previous paragraph (No. 5) for forecastles only of the 
same length. Thus, did the length of the poop equal J erection, 
the deduction would be y^ of freeboard for the vessel flush 
decked = f inch. 

7. In vessels with raised quarter decks only, not less than 
4 feet high, the deduction is at the same rate as in the preceding 
paragraph (No. 6). 

8. In all vessels when the topgallant forecastle is not closed 
at the after end by an efficient bulkhead, the length is never to 
be estimated at a greater full value than ^ of the length of the 
ship, but any extension beyond this may be estimated at one- 
half the value. For example, a vessel 200 feet long has an 



262 KNOW YOUR OWN SHIP. 

open forecastle J of the length of the ship, or 50 feet ; its 
value for deduction is 25 + 12|^ = 37J feet. When the top- 
gallant forecastle has an efficient bulkhead with an elongation 
abaft that bulkhead, the full allowance is given on the entire 
length of the closed-in portion, and afterwards according to 
the previous example. 

9. When the poop has no bulkhead, one-half its length is 
allowed for at the rate of a closed poop. 

10. For bridge houses extending from side to side of the 
vessel, when closed at the fore and open at the after end, with 
all deck openings, doors, etc., properly protected, f of the length 
is estimated as the value for deduction. When both ends of the 
alleyways are open, one-half of the length is estimated as the 
value for deduction. 

Note* — Although it is possible to have occasional gales in the summer season 
as severe as any in winter, yet it is quite unnecessary to remind anyone 
acquainted with the sea that it is in the latter of these seasons that boisterous 
weather is looked for. And thus in summer, when the danger from the 
weather is decreased, there is no reason why a vessel should not be allowed, 
to some extent, to carry more cargo than in winter. The Board of Trade, 
therefore, allow a deduction from the winter freeboard for summer voyages, 
amounting from 1 to 9 or more inches. Summer voyages from European and 
Mediterranean ports are to be made from April to September inclusive. In 
other parts of the world, the reduced freeboard should be used during the 
corresponding or recognised summer months. Double the above reduction to 
be allowed for voyages in the fine season in the Indian seas, between the 
limits of Suez and Singapore. Vessels, up to and including 330 feet in length, 
engaged in North Atlantic trades, are required to have an addition of 2 inches 
to their freeboard, from October to March inclusive. 

A few examples illustrating how the freeboard is ascertained 
for diflferent types of vessels may be helpful in showing the 
practical application of the freeboard rules, etc. 

Let it be understood that by Tables A, B, C, and D is meant 
the freeboard as specified by the Board of Trade for vessels of 
various types. 

Table A. — Flush-decked vessels of the one-, two-, and three-deck type. 
Table B. — Spar-decked vessels. 
Table C. — Awning-decked vessels. 
Table D. — Sailing-ships. 

Example I. 

Flush-decked screw steamer, 300 feet long, 38 feet broad, and 
21 feet depth moulded (no account is taken for any erection re- 
quired for this vessel). 

Sheer forward, 8 feet. 

Sheer aft, 3 ,, 

Coefficient of fineness, 0*8. 

Wood deck on upper deck, 4 inches thick. 



FtlBBBOABD. 263 

Ft. In. 
By Table A, for 21 feet depth moulded, the freeboard is, . . 4 3 
Tne mean sheer, by rule, for a vessel 300 feet long is, 

H^ + 10 = 40 inches! 
10 

In the example the vessel has 8 feet inches sheer forward, 

and 3 , , „ sheer aft, 

2) 11 „ „ 

5 ,, 6 ,, =66 inches mean 

sheer, 

which is an excess of 66 - 40 «= 26 inches (only half of 

40* =» 20 inches is allowed), therefore, 

20 

— — 5 = reduction in freeboard, ... 5 . 

4 ' 



The freeboard 4 feet 3 inches from Table A was for a vessel 252 
feet long. A correction of 1 '2 feet per 10 feet of additional 
length must now be made and added to the freeboard. 
300 - 252 = 48 

M X 1-2 - 676, about 5| inches, . 
10 » * I 

Winter freeboard from top of wood deck, 
Deduct the thickness of the wood deck less the thickness of the 
stringer plate (4 inch), 



Less for summer. 



3 10 





5i 


4 


3i 
3i 


4 


2} 


3 


91 



Summer freeboard measured down from the top of the stringer \ 
plate at the side of the vessel at the middle of the length, j 

Example II. 



This vessel is identical in every respect with Example I., 
except that she has a raised quarter deck 4 feet high and 100 
feet long, connected with a bridge house 80 feet long, with closed 
ends, and a topgallant forecastle 30 feet long closed at the after 
end. The upper deck is iron uncovered with wood. 

These erections altogether measure 100 + 80 + 30 = 210 feet. 

210 7 



308 10 



erections. 



If we turn back to the remarks on Erections in this chapter 
7 
we find that — erections are allowed a reduction in the freeboard 

equal to — - of the allowance for a complete awning deck. 

* See Sheer, 



264 KNOW YOUR OWN SHIP. 

Ft. In. 
By Table A, the freeboard of the vessel flush decked Is, . . 4 3. 
The correction for additional sheer is, 6 J 

3 8J 

By Table C, for a depth of 21 feet, the freeboard is, . . . 2 2 

(No account is taken of additional sheer in awniug-decked vessels.) 

The allowance for a complete awning deck is, . . . . 1 6) 

63 7 

— — of 1 foot 6i inches = about 11 ^ inches = allowance for — - erections. 

Now let us total up all the deductions. 

1. Deduction for excess of sheer = 6^ 

2. Deduction for -^ erections = 11 i 

3. Deduction for the thickness of a wood deck (less thickness of 

stringer plate) when the upper deck is of iron, and covered by 

— or more of substantial erections, 3^ 

10 

Deductions, . . . . 1 9} 

We have still to make the correction for excess of length. 

—• X 1*2 = 6 '76. But only one-half of this should be taken, 

10 '' 

since the deck is covered by over — erections. 

^ 10 

6'76 -r 2 = 2*88 = 2i inches to be added to the freeboard, there- 
fore the nett deduction will be 1 foot 9 J inches less 2| inches 
= 1 foot 6| inches. 

The freeboard by Table A is, 4 3 

The deductions amount to, 1 6| 

Winter freeboard, 2 8J 

Less for summer, 2$ 

Summer freeboard measured down from the top of the 
stringer plate at the side of the vessel at the 
middle of the length, 2 5| 



Example III. 

This vessel has the same dimensions as Example I., with a 
poop 50 feet long, a bridge house 60 feet long, and a topgallant 
forecastle 40 feet long. 

Iron upper deck uncovered with wood. 

Coefficient of fineness = (3*8. 

The bridge house is closed at the fore end with an eflBcient 
bulkhead, but open at the aft^r end. Three-quarters of its length 
will, therefore, be reckoned in\the erections. J of 60 = 45 feet. 



FBBEBOAHD. 265 

Total erections, 50 + 45 + 40 = 135. 

135 4 

300 = 10 «^««*^^^«- 

The mean sheer at one-eighth the length from each end of 
the vessel is 40 inches. 

Ft. In. 

By Table A, the freeboard is, 4 3 

The mean sheer by the Rale is 30 inches. 

40 - 30 = 10 excess of sheer, — = 2J redaction in freeboard, . 2^ 

4 

4 OJ 
Correction for length (added), 5f 

4 6J 

By Table C, the freeboard is, 2 2 

Correction for length, at the rate of 0*6 foot per 10 feet, is 

1? X 0-6;= 2| to be added, 2f 

2 4| 

By Table A, after corrections for sheer and length have been 

made, the freeboard is, 4 6J 

By Table C, after correction for length only has been made, the 

freeboard is, 2 4f 

Allowance for complete awning deck = 2 IJ 

The redaction in freeboard for — erections is h of the allowance 

10 

for a complete awning deck = ^ of 2 feet 1} inches = 8^ 

inches. 

By Table A, after the corrections for sheer and length have been 

made, the freeboard is, 4 6J 

Reduction for — erections, 8i 

10 ' : 

3 9| 
Reduction for wood deck ^ of 3^ = 1^ 

Winter freeboard, 3 8J 

Less for summer, 2| 

Summer freeboard measured down from the top of the 
stringer plate at the side of the vessel at the 
middle of the length, 3 5| 

Example IV. 

Spar-decked steamer 260 feet long, 36 feet broad, and 24 feet 
depth moulded. 

Height of spar deck above main deck, 7 feet. 



266 KNOW YOUR OWN SHIP. 

Spar deck laid with wood deck 4 inches thick. 

Coefficient of fineness = 0*8. 

Depth moulded to main deck = 17 feet. 

Ft. In. 
By Table B, for 17 feet depth moulded, the freeboard is, . . 6 4 J 
This is for a length of 288 feet. A correction must be made for 
decrease in length at 1 inch per 10 feet, and subtracted from 
the freeboard. . 

288 - 260 = 28. 

2? X 1 = 2-8 = about 2i inches, . . 2i 

Winter freeboard from top of wood deck, . 
Reduction for wood deck less thickness of stringer plate, 



6 


IS 
81 


6 


lOJ 
3 



Winter freeboard, 

Reduction for summer, 

Summer freeboard measured down from the top of the 
stringer plate at the side of the vessel at the 
middle of the length, ^ 7^ 



Example V. 

Awning-decked vessel 230 feet long, 32 feet broad, and 17 feet 
depth, moulded to main deck. 

Height from main deck to awning deck, 7 feet. 
Coefficient of fineness, 0*8. 
Mean sheer, 35 inches. 
Iron awning deck. 

Ft. In. 

By Table C, for a depth of 17 feet, the freeboard is, . ' . . 6 li 

230 
The mean sheer by the Rule is — + 10 = 33, and this vessel 

^ 10 ' 

having sheer in excess of the Rule, no correction is made. 
This freeboard is for a vessel 204 feet long. A correction of 
0*5 per 10 feet of additional length must be made, and 
added to the freeboard. 

230 - 204 = 26. 

2? X 0-6 = li inches, .... \\ 
10 1 

Deduction for thickness of wood deck less the thickness of 
stringer plate when awning deck is of iron, .... 

Winter freeboard, 

Less for summer, .... 

Summer freeboard measured down fr* 
stringer plate at the side of 
middle of the length, 




PRSBBOARD. 267 



Example VI. 

Sailing-vessel 200 feet long, 34 feet broad, 19 feet deep. 
Mean sheer, 40 inches. 
Wood deck, 3 J inches thick. 
Coefficient of fineness, 0*7. 

Ft. In. 
By Table D, for 19 feet depth the freeboard is, . . . . 3 10 

The mean sheer by the Rule is — — + 10 = 30 inches. 

40 - 30 = 10 inches excess of mean sheer. 

— = 2J inches reduction in freeboard, . . 2J 
4 

3 7i 
The length by the Rule for 19 feet depth is 190. A correction 
must be made at the rate of 1*2 inches per 10 feet excess 
of length, and added to the freeboard. 
200 - 190 = 10 feet excess of length^ 

— X 1 '2 = about li inches to be added to the freeboard, 
10 

Freeboard from top of wood deck, 

Deduction for thickness of wood deck less the thickness of stringer 
plate, 

Summer freeboard measured down from the top of the 
stringer plate at the side of the vessel at the 
middle of the length, 

Note. — "Wherever definite rules have been quoted in the chapters on 
Tonnage and Freeboard, it will be clearly understood that they have been 
** extracted *' from the Board of Trade instructions to surveyors. 





li 


3 


81 




3 


3 


51 




268 KNOW YOUB OWN SHIP, 

TABLE OF NATDBAL SINES AND COTANGENTS. 

Co- I De- De- 



4-41S3 
4-33U 
4-2468 



ia-0811 
17-8105 
16-3498 
15-2570 

u-sooe 



7 ■5967 
7-3478 
7-1163 

e-BBU 
6-4971 
6-3137 
e-1402 
5'9757 



g™e. '■"Sl"^ ■^'""Bi^"'' gfii 



3-605B 
3'5457 
3-4874 
3'4308 



2-9886 
2-94fia 
2-9042 



27852 
2-7474 
2-7106 
2-6746 



2-4750 
2-4443 
2-4142 
2-3847 



1-6976 
1-B808 
1-6642 
1-6479 



1-4550 
1-4*14 

1-4281 



Tablb op Natural Sink akj> Cotaitokntb [amlintad). 



Do. 


Blue. 


Co- 


De- 


Do- 


Siae. 


Co- 


De- 


De. 


Sine. 


00- 


Da. 


eree. 


tongent. 


gree. 


graB 


tBEgent. 


fiUfl 


gree. 


UDgent. 


gree. 


38 


■5B77 


I'37e3 


54 


48 


■7«1 


-9004 


42 


60 


■8880 


■6778 


30 




■5S13 






4St 


-7480 


■S925 


411 




■8681 


-5715 






■594S 


1'3514 




id 


■7489 


■8847 


4l| 




■8703 


■6657 






■5983 


1^3391 




48} 


•7518 


■8769 


4lJ 




■8724 


-fiUOO 




37 


■6018 


1-3270 


63 


49 


■7647 


-8692 


41 


61 


■8746 


-5543 




371 


■6052 


1^3150 




m 


■7575 


■8616 


403 


61i 


■8787 


-5486 




m 


■8087 


1^3032 




491 


■7604 


■8540 


Sj 


6li 




■5429 




87| 


■8122 


1-2915 




491 


■7632 


-8465 


6l| 




■6373 




SS 


-6158 


I -2799 


52 


50 


7680 


■8391 


40 


62 


-8829 


■6317 






•6190 


1-2884 


513 




7688 


■8316 








■5261 


273 




■6225 


1-2571 






■7716 


■S243 






■8870 


-5205 


27I 




■0259 


1-2469 


6l| 




■7743 


■8170 


39J 




■8890 


-5160 


27} 


38 


■6293 


1-2S48 


61 


61 


■7771 


■8097 




63 


■8910 


-5095 


27' 




■6S27 


1^223e 




5]|. 


■7798 


■8025 






-8929 


■50*0 


26? 




■6360 


1^2130 




5lf 




-7954 






■S949 


■4986 


m 




■6394 


1^2023 




Bl| 


■7853 


-7883 






■8988 


■4931 


m 


40 


-6427 


1^19I7 


60 


52 


■7880 


■7812 


38 


64 




•4877 


28^ 




■6401 


M812 






-790ii 


■7742 


37f 


64i 


■9006 


■4823 








11708 






-7933 


•7673 


374 


Ml 


■9025 


■4769 






•6527 


1-1605 






■7960 


■7604 


37| 


64| 


■9044 


■4716 




41 


■6560 


1-1503 




53 


■7986 


■7535 


37 


65 


■9083 


■4663 


25 


41i 


■6593 


1^1402 


481 




■S012 


■7467 


363 




■9081 


■4610 


243 


«i 


■6826 


1^1802 


iM 




■8038 


■7399 


36l 




■9099 


■4557 


24! 


4l| 


■6653 


l-]20i 


481 




-8064 


■7332 


3b| 




■9117 


•4504 


241 


42 


■6691 


i^iioe 




64 


■8090 


■7266 


36^ 




■9135 


■4452 


24 




•6723 


1-1091 


475 


Mi 


■3115 


■7! 98 






■9153 


■4400 






■8755 


1^0913 


475 


541 


■814] 


7132 






-9170 


■4348 






■arisa 


l-OSl? 


*71 


541 


■8166 


7067 






-9187 


■4298 




« 


■6819 


1-0723 


47 


Sb' 


-8191 


700a 


35 


fi7 


■D205 


■4244 


23 




•6851 


1-0630 






■8216 


■6937 


343 


67J 


■9^22 


■4193 






■6883 


1-0537 






■8241 


■6872 


34| 


m 




■4142 






■6915 


10446 






■8265 




34| 


67| 


9256 


■4091 




44 


•6948 


1^0355 


46 


66 


-8-290 


■6745 


34^ 


68 


9271 


■4040 


22 


44i 


■6977 


1-0265 


46| 




•8314 


■8681 






9288 




213 


id 


■7009 


1-0170 


43 




■S338 


■6618 






9304 




2U 


44j 


7040 


1-0087 


4^ 




-8362 


■6556 






9320 




2l| 


45 


-7071 


1-0000 


46 






-6494 


S3 




■9836 


■3838 


21 




■7101 


■9913 




67i 


■8410 


•6432 


323 




■9351 


■3788 


20? 




■7132 


■9826 




57| 


■8433 


■6370 






9368 


■3738 


^ 




■7183 


■9741 




575 


-8457 


■6309 






9381 


■3689 


M 


46 


■7193 


■9656 


44 


58 


■8480 


■6248 


32 




9396 


■36^9 


20* 


m 




■9672 




581 


■8503 


■6188 


3l| 




9411 


-3590 




*H 


■7263 


■9489 




58f 




■6128 


3]| 




9426 


-3541 




4i 


■7283 


■9407 




es| 


■8649 


■6068 


3l| 




9440 


■3492 




if 


7313 


■9325 


43 


59 


■8571 


■6008 


31 


71 


9455 


-3443 


19 


471 


■7343 


'9243 




59i 


■8694 


■5949 




711 


9469 


■3394 


1B3 


^^S 


•7372 


-0163 




59j 


■8616 


■5890 




"1 


9483 


-3346 


m 


47i 


■7402 


■9083 


421 


59| 




-B83I 


30| 


7]| 


9496 


■3297 


iM 


grea. 


Coilue. 


Tangent. 


De. 
gniB. 


De- 


CoslTB. 


Tangent. 


De. 


A 


toslne. 


TflEgenL 


gnw. 



270 KNOW TOUR OWN SHIP. 

Table of N*TttBAL Sinib amd Cotasoests (amHitued). 



lUent. gtet. eti 



Coiina. TKngent 



CALCULATIONS. 271 



CHAPTER X. (Section I.) 

CALCULATIONS. 

Contents. — Useful Tables and Rules — Calculation of Weight of Steel Plate — 
Solid Stanchion — Hollow Stanchion— Gallons in Fresh- Water Tank — 
Tons in Coal Bunker — Rectangular Barge's Displacement and * * Tons per 
Inch " Immersion — Simpson's Three Rules and Graphic Explanations — 
Calculation of Area of Deck or Waterplane — "Tons per Inch" Immer- 
sion of Ship's Waterplane — Ship's Displacement — Centre of Gravity of a 
Waterplane, Longitudinally or Transversely — Centre of Buoyancy, 
Vertically and Longitudinally — Moment of Inertia — Transverse Meta- 
centre above Centre of Buoyancy — Centre of Gravity — Longitudinal 
Metacentre above Centre of Buoyancy — Alteration of Trim — Area of 
Section and Volume and Centre of Gravity of Wedge of Immersion or 
Emersion — Centre of Effort, 

USEFUL TABLES, RULES, AND PRELIMINARY 

CALCULATIONS. 

Useful Tables. 

I cubic foot contains 6^ gallons. 

1 ,, ,, of fresh water weighs 1000 ozs. or 62 J lbs. 

1 „ „ of salt „ „ 1025 „ 64 „ 

In some localities, where the water is brackish, its weight per 
cubic foot is between 1000 and 1025 ozs., and in other localities, 
such as the Red Sea, a specific gravity of over 1*025 is found. 

36 cubic feet of fresh water weigh 1 ton. 

35 ,, ,, salt ,, ,, ,, 

40 to 50 ,, ,, coal ,, ,, 

1 ,, foot steel weighs 490 lbs. 

1 ,, ,, wrought-iron ,, 480 „ 
1 ,, „ cast-iron ,, 454 ,, 

Steel plates and bars are therefore about 2 per cent, heavier 
than iron plates. 

The thickness of steel plates is usually given in twentieths of an 
inch, and the thickness of iron plates in sixteenths of an inch. 

A square foot of steel plate 1 in. thick weighs 40 lbs. + 2%. 
Therefore a square foot of steel plate ^ in. thick weighs 2 lbs. + 2%. 
A square foot of iron plate 1 in. thick weighs 40 lbs. 
Therefore a square foot of iron plate -^ in. thick weighs 2^ lbs. 



272 



KNOW TOUR OWN SHIP. 



Timber- 



cubic foot of elm 

red pine 



ft 

>» 

}) 

yt 
ft 
tt 
it 

n 



112 lbs. 
2240 „ 
20 cwts. 
] 2 inches 
3 feet 



pitch pine 
yellow pine 
greenheart 
lignum vitse 
English oak 
Riga oak 
Dantzic oak 
Indian teak 
African teak 

= 1 cwt. 
= 1 ton. 

= 1 ft 

= 1 foot I 

1 yard 



)) 



tt 



ft 



weighs 84 lbs. 
36 
41 
28 
62J 
83 
52 
43 
47 
55 
61 



tt 

19 
tt 

it 
it 
»t 
tf 



Measurement of length. 



144 square inches = 1 square foot | 

9 ,, feet =1 ,, yard \ 

1728 cubic inches = 1 cubic foot ) 



= 1 



ti 



yard 



it 



it 



it 



ti 



area. 



volume. 



it 



cubic 



>f 



27 „ feet 

Definitions — 

Area is measurement in square yards, square feet, or square inches. 
Volume ,, ,, cubic ,, cubic 

Weight „ ,, tons, cwts., lbs., etc. 

Circular Measure 1 degree = '01745. 

Useful Rules. 
To find the area of the following figures : — 
I. 



-VST 

I 

a 

X. 



L X B = area. 



-- L --*i 



II. 



III. 




W A ->! 



— A >^ 

X 




I 



B > 




Note. — Opposite sides parallel. 
A X B = area. 



Note. — Sides A and B parallel. 

A + B ^ 

— t: — X C = area. 



-B--*\ 




A X B 



= area. 



V. 







D2 X 7854 = area. 



CALCULATIOKS. 



273 



y. 



Vl. To find circumference of a circle. 

D X 3*1416 or D X 3f = circumference. 
VII. To find the volume of an object, the length of which is 
given, and the section of which is uniform throughout, the 
section being like either I., II., III., IV., or V. 
Rule — Multiply the area of the section (or one end) by the 
length — the product gives the cubic contents. 

To find the cubic contents of an object of b 
the following elevation, the breadth being -* 
constant throughout the length. 1*" ^ 

Find the area by Rule III. (B and b being parallel), and 
multiply by the breadth. 

—^ — X L X breadth = cubic contents. 

VIII. To find the volume of a spherical object, the diameter D 

being given. 

D3 X -5236 = volume. 

USEFUL RULES AND PRELIMINARY CALCULATIONS. 

Example I. 
Find the weight of a steel plcUe as per sketch, -^j^ thick, with 
a circular hole, 2 feet diameter punched out. 

5 + 3 

— ^— X 6 = 24, area of plate 6 feet long. 



4x5 



= 10, 



2 ' " " 

2^ X '7854 = 3'1416 area of circular hole. 
(24 + 10) - 3-1416 = 30-85 area of plate. 
1 square foot ^ = 18 lbs. weight. 




30-86 X 18 = 655-3 + 2 % = 555-3 + 11 = 566-3 lbs. weight. 

Example II. 

To find the weight of a solid iron standwm 20 feet long, 3 
inches diameter. 

3 inches = -25 of a foot. 
•262 X -7864 X 20 X 480 = 471 '24 lbs. weight. 

Example III. 

To find the weight of a hollow iron stanchion 4 inches outside 
diameter, 2 inches inside diameter, and 10 feet long. 

The mean width of plate which would form this stanchion = 
3 inches x 3-1416 = 9*42 inches. 

Width. Thickness. ^^^^^ 
0-42 X 1 X (10 X 12) = 1130-4 cubic inches. 



1130-4 
1728 



X 480 = 314 lbs. weight. 




274 KNOW YOUR OWN SHIP. 

Example IV. 
To find the number of gallons and tons of fresh water a tank 
will contain. The dimensions are: — Length, 12 feet; breadth, 6 
feet; depth 7*3 feet. 

12 X 6 X 7*3 = 525 '6 cubic feet in tank. 

625*6 X 6 '25 (gallons in 1 cubic foot) = 3285 gallons contained in tank. 

525*6 

-_-- = 14*6 tons of water contained in tank. 
36 

Example V. 

How many tons of coal zcill a coal bunher contain at 45 cubic 

feet per ton ? It is 30 feet long, 10 feet broad, 13 feet deep. 

30 X 10 X 13 „^ ^ , 

T^ = 86-6 tons. 

45 

Example VI. 

Whai is the displacement of a rectangular barge 60 feet long, 
20 feet beam, and 6 feet depth 1 It draws 4 feet aft, and 3 feet 
6 inches forward in fresh water. 

4-0 + 3*5 „ ^- J vx 
5 = 375 mean draught. 

60x20x375 .„- , ,. , . 
5^ = 125 tons displacement. 

Example VII. 

The same barge in a light condition draws 1 foot fore and aft. 
What weight or cargo is there on board ? 

— = 33 '33 tons, displacement light. 

Therefore 125 - 33*33 = 91*67 tons weight on board. 

Example VIII. 
How many tons would be required to increase the draught of this 
barge 2 J inches ? 

60 X 20 „.or: . . , 

2 '85 X 2*5 = 7*125 tons to increase draught 2 J inches. 

Example IX. 

What would be the increase in draught if 12 tons were placed on 

board ? 

12 
^ „^ = 4*21 inches increase in draught. 
2*85 ° 

Example X. 

To find the area of such a figure as this, which is similar to 

half of the deck of a ship or a h^ toaier^ 
^^\ plane. Such areas are found by what 

^ 60' or- >- 




^L A - kn'k. - - -- -J' are known as Simpson's Rules. 



CALCULATIONS. 



275 



Simpson's First Rule. — ''Divide the hose into any even 
number of eqtcal lengths" say 6, then ^ = 10 feet each length, 
" through these points draw ordinates to the curve, which ordinates 
toill consequently he odd in number," in this case, including the 
endmost ordinates, there are 7. " Multiply the length of each 
of the even ordinates by 4, and each of the odd ordinates by 2, 
excepting the first and last, which multiply by 1. The sum of 
these products multiplied by ^ of the common interval between the 
ordinates will give the area required." 

The calculation could be arranged in either of the following 
ways {the 1th ord, in the diagram is supposed to be 1 foot) : — 



No. of Ord. 


Ord. 


« 2 

33 


3-8 


o 

% 4 
» 6 


7-0 
4-0 



No. of 
Ord. 



14-8 



Sum of even 
ordinates. 



29 '6 -f ^^^^^ ^^°^ ^^ 
\ even ordinates. 



Q 

O 

Q 
Q 

o 



1 

3 
5 

7 



•0 Half of Ist ord. 
6*2 
6-0 

•5 Half of last ord. 



4 
5 
6 

7 



Ord. 


S.M. 


0-0 


1 


3-8 


4 


6-2 


2 


7-0 


4 


6'0 


2 


4-0 


4 


10 


1 



Products or 
Functions. 



0-0 
15-2 
12-4 
28-0 
12-0 
16-0 

10 



84*6 Sum ofpro- 
ducts. 
^ common interval V* -= 3*33 



42*3 Sum of products obtained by 
treating the ordinates by the 
Multiplier for half Simpson's Multipliers. 

Simpson's 
whole Mul- 
tipliers 2 

84*8 Sum of products. 
^ common 
interval J^= 3 33 



2538 
2538 
2538 



281-718 Area. 



This method is more 
commonly adopted in 
actual practice. 



2538 
2538 
2538 



281-718 Area. 



276 



KNOW YOUR OWN SHIP. 



Simpson's Second Rule. — ''Divide the hose into equal 
lengths, so that their number toill be a multiple of 3," in this case 
(see figure) 6 lengths. " Through these points of division draw 
ordinates to the curve, the total number of which, when divided by 
3, gives a remainder of l,^* There are seven ordinates, |^ = 2, and 
a remainder of 1. ** Call the ith (and if there had been more than 
7 ordinates), the 7th, 10th, 13th, etc., ordinates, dividing ordinates, 
and the others, excepting the first and last ordinates, intermediaie 
ordinates. Add together the first and last ordinates, twice the 
dividing ordinates, and three times the intermediate ordinates. 
Multiply the sum by ^ of the common interval (10 feet), and the 
product will be the area of the figure nearly. 

The calculation is usually arranged as follows : — 



No. of Ord. 


Ord. 


S.M. 


Functions or Prodncts. 


1 


0-0 


1 


0-0 


2 


3-8 


3 


11-4 


3 


6-2 


3 


18-6 


4 


7-0 


2 


14-0 


5 


6-0 


3 


IS'O 


6 


4-0 


3 


12'0 


7 


1-0 


1 


0-0 



f common interval = f of 10 = 



74-0 
375 

1500 
2625 



277*50 Area. 



It will be observed that the result is 4 square feet less than by 
the 1st Kule. The latter is preferable when the number of 
ordinates is such as to permit of the 1st Rule being applied. 

Simpson's Third Rule is for finding the area of a part of a 
.D figure such as shown in the adjoining diagram. 
It is required to find the area of the part 
C A E F {the 14 feet ordinate = GH), 
^ ^ Let A E = 15 feet. Make E G = 15 feet also, 

''^ /s'cC-^ /5'(f» "^ and draw G H to the curve. 

Rule. — Add together five times the near end ordinate (A O) and 
eight times the middle ordinate {EF), From the sum subtract the 
far end ordinate {G H), and multiply the remainder by ^ of the 
common interval. The product vyill give the area required. 




CALCULATIONS. 



277 



The calculation is arranged as follows : — 



8 X 5 = 40 
12 X 8 = 96 



136 sum. 
Subtract 14 



122 remainder. 
5^5 common interval = f| = 1 '25 

610 
244 
122 



152 '50 area required. 




Interval 



Interval"^ 



By the following graphic method it is hoped that the applica- 
tion of the foregoing Simpson's Rules will be more comprehensive. 

First Rule. — Here is a figure, say, a piece of a ship's deck 
A B is the fore and aft middle line, and 
D C the curve of the deck. To find its 
area by Simpson's First Rule, AB is 
divided into two equal parts at the 
point E, and E G is drawn to the curve. 
By this rule, the first and last ordinates, 
B C and A D, are always multiplied by 
1, and the second ordinate (that is, the even ordinate) is multiplied 
by 4. Then these products are multiplied by \ of the common 
interval, that is, ^ of A E — E B. 

Splitting this calculation up into its separate parts or steps in 
the mode of procedure, we get : — 

ADxiofA£ = area of A D J E. 
EGx|rofAE = area of G E H F. 

But this second ordinate G £, according to the rule, has to be multiplied 
by 4. 

. '• 4 (E G X ^ of A E or E B) = area of the 4 rectangles contained in 
OKLS. 

Then, finally, BCx|ofEB = area of L B C M. 

The sum of these three parts gives the area of the whole figure A B G D. 

It will be noticed in this calculation that a piece of the area of 
the curve is lost over the rectangle A D J K, but a piece is gained 
within the rectangle at the other extremity M L B C. Similarly, 
a piece of the area of the curve is lost over the two rectangles 
GELS, and a piece gained within th^ rectangles K E G, 



278 



KNOW YOUR OWN SHIP. 



The areas of the two pieces gained and the two pieces lost 
approximately balance each other. 

While this rule approaches very nearly to the truth, it is not 
absolutely correct. However, for all practical purposes, and in all 
ship calculations, when the rule is carefully applied, the error is 
so slight as to be unnoteworthy. 

Where a figure is divided into a considerable even number of 
equal spaces, the rule applies in exactly the same manner as just 
described. For the first two spaces the multipliers are 1, 4, 1, 
and for the second two spaces the multipliers are 1, 4, 1, and so 
on. 



1 
1 



1 

1 



1 
1 



142424241 

To give a practical example illustrating what has been explained, let 
A B = 18 feet, A D = 4 feet, E G = 6 feet, and B C = 7 feet The common 
interval between ordinates = -i^ = 9 feet, and one-third of the common 
interval = 3 feet. 



4x3 

4(6 X 3) 
7x3 



12, area of A D J K. 

72 ,, the four rectangles contained in E L S, 

21 .. L B C M. 



105 



f» 



If 



whole figure. 



Arranged in the usual form, and as previously described. 



No. of Ord. 


Ord. 


S. M. 


Products. 


1 
2 
3 


4 
6 

7 


1 
4 
1 


4 
24 

7 



J common interval = f = 



35 
3 

105 Area of whole figure. 



Simpson's Second Rule. — With the explanatory notes upon 
Simpson's First Rule, the reader will be able to follow the graphic 
explanation here given for Simpson's Second Rule. 

Simpson's Multipliers are 1, 3, 3, 1, making altogether 8 oblongs 
and 3 intervals. 1 oblong is as long as the first ordinate^ 3 $U9 



CALCULATIOKS. 279 

long as the second ordinate, 3 aa long as the third ordinate, and I 




( the part of the figure the 



Wwtt 



Simpson's Third Rule. — C DAB 

area of which is foimd 
by this rule. 

Simpson's Multipliers 
are 5, 8, and 1, which 
latter product haa to be 
deducted. There are, 
therefore, 6 + 8 - I = 
12 oblongs, 5 of them 
are of the length of the 
ordinate AD, 8 of the 
length of the ordinate 
B C, which includes 1 

oblong more than the ' "" 

required number to cover the area ADCB. The \ 
Delect the black wedge at their upper extremities, while the 
8 oblongs gain a wedge outside the curve. By deducting the last 
ordinate E F, the surplus oblong to the right of B C is corrected, 
while the excess in length of the ordinate E F over B C produces 
an area indicated by a black oblong, which together with the 
lost wedge over the first 5 oblongs approximately neutralises the 
excessive area obtained over the next 7 oblongs. The width of 
on oblong is y'^ of the tehole intei-val. 

A study of the foregoing diagrams, showing the application of 
Simpson's Rules, indicates clearly that the nearer the ordinatea are 
spaced to each other, or, in other words, the more intervals into 
which an area ia divided, the nearer does the calculation approach 
to accuracy. Supposing the area of a ship's deck, 200 feet long, 
be divided into 1 2 interi'als, a stiidy of these rules will further 
show that, while they apply with great accuracy to the middle 



280 



KNOW TOUR OWN SHIP. 



f length or more, the sudden curve of the ends of the deck towards 
the stem and stem, especially in a bluff cargo vessel, renders 
the calculation far from even approximately accurate for these end 
areas. 

Let the adjoining figure represent the after 33*33 feet of this deck, 

covering exactly 2 



intervals. The 
black wedges in- 
dicate the area 
within the deck 
line which is in- 
cluded by the rule, 
and the hatched 
areas indicate the area outside the deck line which is gained by the 
calculation. The inadaptability of the rule, as previously given, 
to apply to such an area as this, with any degree of accuracy, 
is obvious. But by a modification in the application of the 
rule itself, this inaccuracy can be largely obviated. 

As previously stated, the closer the ordinates are spaced, the 
greater the degree of accuracy obtained. By this process of ap- 




'^ 'l$gg ^2- iB-ee *"' 







2 half 1% 
-interra} — tep*- 



whole 4! 

t'n terra/ 



plication of the first rule, the first interval is subdivided, and 
an ordinate measured at the point of division. Simpson's 
Multipliers now become half of what they were originally, viz., 
J, 2, ^. In other respects the calculation is carried out in the 
usual manner. Simpson's Multipliers are now : — 

J 2 i (See accompanying 

14 1 diagrams). 



i 2 li 4 1 

By this method of subdivision of the intervals the discrepancy 
between the excess and loss of area of the deck is reduced, and 
by means of a still further subdivision the error can be lessened. 



CALCULATIONS. 



281 



Example 11. 

To Calculate an Area by Introducing Subdivided Intervals. — The 
half ordinates for a ship's waterplane at, say, the load line, are 
2, 8,* 12, 14, 16, 17, 16-6, 15, 11, 7,* 0, ordinates 8 and 7 being 
subordinates (half-ordinate means ordinate for half width of water- 
plane). The common interval is 18 feet. Find area of whole 
waterplane. 



No. of Ord. 


i Ord. 


S. M. 


Products, 


1 


2 


i 


1 


14 


8* 


2 


16 


2 


12 


14 


18 


3 


14 


4 


56 


4 


16 


2 


32 


5 


17 


4 


68 


6 


16-6 


2 


33*2 


7 


15 


4 


60 


8 


11 


14 


16-5 


H 


7* 


2 


14 


9 





4 






314-7 
J common interval = ^ = 6 



Area of half waterplane 1888 '2 
Multiplier for both sides 2 

Area of whole waterplane 3776*4 

Example 12. 

To Find the " Tons per Inch " Immersion of the Foregoing Vessel 

3776*4 

at the Load Line, tstt- = 8*99 " tons per inch " immersion. 

420 

By means of Simpson's Rules, the area of any waterplane, deck, 
or transverse section of the hull of a ship is easily found, whatever 
may be the number of intervals into which these areas may be 
divided. 

In such an example as that shown by the figure, where there are 
eleven intervals, neither 
the First nor the Second 
Rule will apply for the 
whole length, but then, by / 2 i" 
making use of the Third 

Rule, the area can be found. Thus, by using the First Rule, the 
area of the whole figure up to the 1 1th ordinate can be found, 
and by using the Third Rule the area of the last space between 




282 



KNOW YOUR OWN SHIP. 



the 11th and 12th ordinates is found. The sum of the two 
parts gives the whole area. 



Example 13. 



BO 



20-2 






Shotos a further Application of 
Simpson's Rules in ascertaining 
the Capacity of a Cross Bunker. — 
The bunker is 20 feet long and of 
constant section throughout its 
length. The ordinates of the 
transverse section are shown upon 
the sketch. Find the quantity of 
coal it [will contain at 45 cubic 
feet per ton. The bottom interval 
is subdivided. 




No. of Ord. 


Ord. 


S. M. 


Products. 


1 


20 


1 


20 


2 


20 '2 


4 


80-8 


3 


20-4 


2 


40-8 


4 


20-4 


4 


81-6 


5 


20-1 


H 


30-15 


H 


18-0 


2 


36-00 


6 


16-0 


h 


8 



297-35 
J of common interval = J of 3 = 1 



297-35 
Multiplier for both sides 2 



Area for both sides 



594-7 

20 Length of banker. 



45)11894 Cubic feet in bunker. 
264-31 Tons in bunker. 



We have shown how Simpson's Rules may be applied to find 
the area of a deck, a waterplane, or a transverse section of a ship. 
In a similar manner, these rules may be used to find the dis- 
placement of a ship floating at a given waterline. 



CALCULATIONS. 



283 



Example 14. 

To Calculate a Ship's Displacement^ \st Method, — She draws 
20 feet of water from the top of the heel. Divide this depth 
into a number of equal intervals, suitable for the application 
of Simpson's First or Second Rule, say, five equal intervals, each 
being 4 feet, with the bottom interval subdivided. The area 
of each of these waterplanes is now calculated as previously 
shown. 



Let the total area of 



No. 1 = 20,000 ! 


square feet. 


„ 2 = 19,500 


i» - 


„ 3 = 18,000 




„ 4 =14,000 




„ 5 = 8,000 




,, 5^ = 4,000 




„ 6 = 1,000 





« 




T — 

'1 « I 




These areas are treated by Simpson's Multipliers ; the sum of 
the products multiplied by J of the common interval (when the 
First Rule is applied) equals cubic feet displacement, and in a 
similar manner the Second Rule may be applied when the intervals 
are suitable. 



No. of Area. 


Area. 


S. M. 


Products. 


1 


20,000 


1 


20,000 


2 


19,500 


4 


78,000 


3 


18,000 


2 


36,000 


4 


14,000 


4 


56,000 


5 


8,000 


H 


12,000 


H 


4,000 


2 


8,000 


6 


1,000 


* 


500 



Common interval 



210,500 
4 



Divide by 3 for J common interval 3)842,000 



35)280,666 Cubic feet displacement 
8,019 Tons displacement. 



"^^^^^^^ 



284 



KNOW TOUR OWN SHIP. 



Example 15. 

To Calculate a Ship^s Displacement, 2nd Method, — Another 
method of finding the displacement is to divide the length 
of the vessel into a number of equal intervals suitable for 
the application of Simpson's Rules. The areas of the transverse 
sections up to the load waterplane are calculated at each of these 
stations, and these areas are put through Simpson's Multipliers, 
and the calculation carried out in a way exactly similar to the 
foregoing examples. 

A vessel, 200 feet long, is divided into twelve intervals, and the 
areas are calculated at each station. The areas are as follows : — 

6, 200, 280, 350, 400, 400, 390, 370, 330, 280, 240, 180, 18. 

The common interval between the areas is — -^ .= 16*66 feet. 

12 



No. of 
Section. 


Area. 


S. M. 


Products. 


1 


5 


1 


5 


2 


200 


3 


600 


3 


280 


3 


840 


4 


350 


2 


700 


5 


400 


3 


1200 


6 


400 


3 


1200 


7 


390 


2 


780 


8 


370 


3 


1110 


9 


330 


3 


990 


10 


280 


2 


560 


11 


240 


3 


720 


12 


180 


3 


540 


13 


18 


1 


18 



I of 16-66 = 



9263 
6-24 



35)57801*12 Cubic feet displacement 



1651-46 Tons. 



ExAMPLB 16. 

To Find the Centre of Gravity of a Waterplane or of a Transverse 
Section of a VesseVs Displacement. — In Chapter II., it has been 
shown how to find the centre of gravity of a number of weights 
ranged along a bar, from a given point. The principle holds good 
in all other calculations for centres of gravity. 

Let the adjoining figure represent a ship's deck, the area of 
which is required. The lengths of the half-ordinates are shown on 
the diagram, and the intervals between the ordinates. Had 1, 



CALCULATIONS. 



285 



10, 12, 8, been weights upon the deck the centre of gravity of 
these weights only would have been found by multiplying each by 
its distance or leverage from one end of the deck, and dividing the 
sum of the moments obtained by the simi of the weights. How- 
ever, though the ordinates are not weights, they serve the same 

purpose as weights, being ^ 

representative of where ^ — ^T^g..^ 

the areas are greatest and ^y^ ^I ^i 

least. But just as in 
calculating the area of a deck, Simpson's Rules are applied in 
order to obtain greater accuracy than would be obtained by 
simply taking the mean of all the ordinates, in like manner, in 
obtaining the centre of gravity of the deck we employ Simpson's 
Rules, and thereby, greater accuracy is obtained by using the 
ordinates multiplied by their respective multipliers as indices of 
the fulness or fineness of the deck, than by using the ordinates 
themselves. The calculation would be done as follows : — 



No. of Ords. 


iOrds. 


S. M. 


Products. 


Leverages. 


Moments. 


1 


1 


1 


1 








2 


10 


4 


40 


6 


240 


3 


12 


2 


24 


12 


288 


4 


8 


4 


32 


18 


576 


5 





1 





24 






1104 
97 



97 
= 11-38 



1104 



The centre of gravity of the deck is 11*38 feet from the left- 
hand endmost ordinate. In practice, it is usual to use only the 
number of intervals for leverages, and multiply the sum of the 
moments so obtained by the interval. This effects a saving in 
figures. By this method the calculation would be as follows : — 



No. of Ords. 


i Ords. 


S. M. 


Products. 


Leverages. 


Moments. 


1 


1 


1 


1 








2 


10 


4 


40 


1 


40 


3 


12 


2 


24 


2 


48 


4 


8 


4 


32 


3 


96 


5 





1 





4 






184x6 
97 



97 
= 11*38 C. G. from first ordinate. 



184 



286 



KNOW YOUR OWN SHIP. 



Example 17. 

To Find the Perpendicvlar Centre of Gravity of a Half 
Waterplane Transversely from the Fore and Aft Centre Line, — Rule. 
— Take the half squares of the ordinates, and treat them by 
Simpson's Multipliers as though they were the ordinates for a new 
curve. The area of this hypothetical curve is the moment of the 
figure relatively to the fore and aft centre line. Divide this 
moment by the actual area of the half waterplane, and the result 
is the perpendicular distance of its centre of gravity from the 
longitudinal middle line of the waterplane. 

The following example will serve as an illustration, the common 
interval between the ordinates being 18 feet : — 



No. of 
Ord. 



1 
2 
8 
4 
5 



Ords. 


S. M. 


Products. 


2 


1 


2 


. 5 


4 


20 


8 


2 


16 


4 


4 


16 





1 






Squares of 
Ordinates. 



4 
25 
64 
16 






Products of Squares 
of Ordinates. 



4 

100 

128 

64 





54 
^ of common interval ■= Jj^ 6 

824 



i squares 2)296 

148 
^ common interval 6 

moment 888 



888 _ n.-A — Perpendicular distance of centre of gravity from 
^^ _ J / 4 — longitudinal centre line. 



Example 18. 



To Find the Centre of Buoyancy or Centre of Gravity ofDutplace' 
ment. — Suppose, first, that it is desired to obtain the height of the 
centre of buoyancy above the keel. 

The draught (measuring from the top of keel) is divided into a 
number of equal spaces in exactly the sam^e way as is done for 
displacement. The area of each of these waterplanes is calculated 
by the application of one of Simpson's Rules. These areas of 
waterplanes are then put through Simpson's Multipliers. Thus 



CALCULATIONS. 



287 



far the calculation has resembled that for displacement. All this 
information may, therefore, be copied direct from the displacement 
calculation, or the displacement calculation itself may be used, as 
is generally done in practice. If the centre of buoyancy is 
required from the top of the keel, the products of areas are 
multiplied by their respective leverages from the top of the 
keel. The sum of these moments divided by the sum of the 
products of areas will give the height of the centre of buoyancy 
above the top of the keel. The steps in this calculation are 
identical with those followed in the previous example for finding 
the centre of gravity of a waterplane, the areas of the horizontal 
waterplanes taking the place of the ordinates of the waterplane. 

As an example, suppose it is required to find the centre of 
buoyancy above the keel of the vessel whose displacement was 
found in Example 14. 



No. of 












Horizontal 


Area. 


S. M. 


Products. 


Leverages. 


Moments. 


Area. 












1 


20,000 


1 


20,000 


5 


100,000 


2 


19,500 


4 


78,000 


4 


312,000 


3 


18,000 


2 


36,000 


3 


108,000 


4 


14,000 


4 


56,000 


2 


112,000 


5 


8,000 


li 


12,000 


1 


12,000 


54 


4,000 


2 


8,000 


i 


4,000 


6 


1,000 


i 


600 





000 



210,500 



Common interval 



648,000 



210,500)2,592,000 
Centre of buoyancy above top of keel = 12*3 feet. 



Example 19. 



To find the fore and aft centre of bvxyyancy the same method 
exactly is adopted, using vertical areas. 

As an example, find the centre of buoyancy of the vessel in 
Example 15. 



KNOW TODS OWN SHIP. 



No. of 
Vwt. Area. 


Area. 


S. M. 


ProdnctB. 


Leverages. 


Momento. 


1 

2 


5 
200 


1 


5 

eoo 





600 




280 




810 




1880 




350 


2 


700 




2100 


6 


400 


a 


1200 




4800 


6 


400 


s 


1200 




8000 


7 


390 




780 




4880 




370 


3 


1110 




7770 




330 




990 




7920 


10 


280 


2 


MO 




eo4o 


11 


240 


3 


720 


10 


7200 


12 


180 


3 


510 


11 


6940 


13 


IS 


1 


IS 


12 


218 



g283)seS,740-86 
Centre of buoyancy from area 1 97'02 feet 

EXAUFLE 20. 
To find the momeni of ittertia of a waterplane (required in 

order to arrive at the height of the transverse metaceotre above 

the centre of buoyancy), relatively to the fore and aft axle pass- 
ing through the centre of gravity 
of the waterplane. Imagine tbe 
waterplane to be divided into an 
infinitely small number of units of 
area. Multiply each one of these 
units of area by the square of its 
distance from the fore and aft centre 
line of the waterplane, which is the 
axis about which the moment of 
inertia is calculated. The sum of 
all these products is the moment of 
inertia required. Let theadjoining 
figure serve as an illustration. Here 
^ we have, say, a midship portion of 
the area of a waterplane. It is 6 
feet long and 9 feet wide, that is, 41 

feet on each side of the fore and aft middle line. Let it be divided 

into unite of area of 1 square foot each, 

Multiply each of these areas by the squares of their reepeotave 

distances from the axis, as follows ; — 





,- 


- 


— 


srf_ 




































1 
















1 


ft^s 














11 
































' 














1 
















1 
















1 
















i 























CALCULATIONS. 


6( 
6< 
61 
6( 
6< 


:-5 X -252) = 
[ 1 X 12) = 

: 1 X 22) = 
: 1 X 32) = 

[ I X 42) = 


•1875 

6 0000 

24-0000 

54-0000 

96-0000 



289 



180*1875 Moment of inertia for one half of plane. 
2 Multiplier for both halves. 

360*3750 Total moment of inertia. 

The moment of inertia is first obtained for the half waterplane 
relatively to the fore and aft axis of the plane, as in the foregoing 
case, and the result is multiplied by 2 for the whole plane — the 
other half being exactly similar when the vessel is upright. 

Thus, on one side, we have : — 

6 half units of area at a distance of *25 of a foot, 
then 6 „ ,, ,, 1 foot 

„ 6 ff „ „ 2 feet, and so on. 

Naturally, as our units of area are not infinitesimally small, the 
result can only be approximate. The smaller the units of area, 
and therefore the greater number of them, the more correct is the 
result. It will be obvious that such a method as this could not 
be applied to such a huge area as a ship's waterplane. 
Rule for Moment of Inertia of a Ship^s Waterplane : — 
Divide the fore and aft axis into a nimiber of equal intervals 
suitable for the application of one of Simpson's Rules. Measure 
the half ordinates at the points of division, and cube each of them. 
Take one-third of these cubes, and deal with them as though they 
were ordinates of a curve, the area of which has to be found. 
Such area would be the moment of inertia of the half waterplane. 
The moment of inertia of the foregoing figure found by this 
method would be as follows : — 



i Ords. 


Cubes. 


S. M. 


Products. 


4-5 
4-5 
4-5 


91*125 
91-125 
91-125 


1 
4 
1 


91-125 

364-500 

91-125 



i of cubes 3)546-750 
I common interval = | = 



182-25 
1 



1 82 '25 Moment of inertia for half plane. 
2 Multiplier for both halves. 



364*5 Total moment of inertia. 



290 



KNOW TOUR OWN SHIP. 



It is now seen that the previous method was only approximate, 
being over 4 less than the correct calculation gives. 

In an earlier chapter, we have shown that the moment of 
inertia of a rectangular waterplane is: — 

Length of waterplane x Breadth* 
12 

therefore, applying this to the same figure 

6 X 9» 



12 



= 364-5, 



which result is similar to that of the last calculation. 

Calculation for Moment of Inertia of aa Actual Ship's Water- 
plane. — To find the moment of inertia of the load waterplane of a 
vessel whose half ordinates are 0, 2*5, 6, 9, 11, 12, 10, 7, 5, 2, *5. 
The common interval between the ordinates is 9 feet. 



No. of 
Ord. 


J Ords. 


Cubes of i 
Ords. 


S. M. 


Moments. 




1 


•0 


•00 


1 


•00 




2 


2-5 


15-62 


4 


62-48 




3 


6-0 


216-00 


2 


432-00 


i 


4 


9-0 


729-00 


4 


2916-00 




5 


11-0 


1331-00 


2 


2662-00 




6 


12-0 


1728-00 


4 


6912-00 




7 


10-0 


1000-00 


2 


2000-00 




8 


7-0 


343-00 


4 


1372-00 




9 


5-0 


125-00 


2 


250-00 




10 


2-0 


8-00 


4 


32-00 




11 


•5 


-12 


1 


-12 





i of cubes 3)16,638-60 
^ common interval = ) = 



5546-2 
3 



16,638-6 M of 1 of i^ plane. 
For both halves of waterplane 2 

33,277 '2 Moment of inertia. 



Example 21. 

To Find the Height of Metacentre above the Centre of Buoy- 
ancy : — 

Moment of inertia of waterplane ^ ^^^.^^^re above centre of buoyancy. 

Displacemeut m cubic feet 



CALCULATIONS. 291 

As an example, suppose the moment of inertia of the foregoing 
example is for a vessel of 300 tons displacement at load draught. 
The height of metacentre above centre of buoyancy would be : — 

33,277 ^S_3^_ 
300 X 35"10,500"^^^^®®^- 



Example 22. 

To Find the Position of the Centre of Gravity of a Vessel in 
Relation to the Metacentre, by Experiment. — This has been 
dealt with, and an example worked out in Chapter VI. (Section 
I.), page 128. 

Let W = weight moved across deck. 

d = distance weight is moved; 

D = displacement in tons. 

W x d 

— y: — = G G' (shift of centre of gravity transversely). 

G G' X cotangent of angle of keel = G M (metacentric height). 

^ . e 1 length of plumb line in inches 

Cotangent of angle = ," . .. ^ ^ , r^p = — -. — ^t- 

° ° mean deviation of plumb line in inches. 

^V X d length of plumb line in in ches _ p » r 

D mean deviation of plamb line in inches" 



Example 23. 

To Find the Centre of Gravity of a Ship by Finding the Distance 
of the Centre of the Weight from^ say, the Bottom of the Keel. — 
Multiply every item of weight in the ship by its distance above 
the bottom of the keel. The sum of all these products or 
moments divided by the sum of all the weights (the total of 
which equals the total weight of the ship), gives the height of 
the centre of. gravity above the bottom of the keel. 



Example 24. 

To Find the Height of the Longitudinal Metacentre above the 
Centre of Buoyancy. — The principle of this calculation is identical 
with that alreaxly given for height of transverse metacentre above 
centre of buoyancy. 

The moment of inertia of the waterplane is found relatively to 
a transverse axis passing through the centre (centre of gravity) 
of the particular waterplane. When this moment of inertia is 



292 KNOW TOUR OWN SHIP. 

found, and divided by the displacement in cubic feet, the result 
is the height of the longitudinal metacentre above the centre of 
buoyancy. 

Here, again, the moment of inertia is the sum of the products 
of each of the units of area in the waterplane, multiplied by the 
square of their respective distances from the transverse axis. 
Were the waterplane rectangular, the moment of inertia would be 
found by identically the same method as in the first two calcula- 
tions in Example 20, excepting that what was in that case the 
length now becomes breadth, and the breadth becomes length. 

Breadth x Length' 9x6' - ^„ i. * • _x- 
r^r — = — — — = 162 moment of inertia. 

Owing, however, to the shape of an actual ship's waterplane, a 
modification in the application of the rule is necessary. 
The method adopted is as follows : — 

let. Find the Moment of Inertia of the Waterplane, Relatively to 
One End of the Waterplane, — Rule, Divide the fore and aft middle 
line into a number of equal intervals suitable for the application of 
one of yimpson's Rules. Through these points draw ordinates to the 
curve. Then multiply each J ordinate by its proper multiplier. 
Each of these products is next multiplied by the square of the 
number of whole intervals it is distant from the end of the water- 
plane. The sum of these moments multiplied by \ or f , the cube 
of a whole interval (according to the Simpson's Rule applied) will 
give the moment of inertia of the \ waterplane relatively to the first 
ordinate. By multiplying by 2 the M of 1 for whole plane is obtained. 

As we require, however, the moment of inertia of the waterplane, 
relatively to the centre of the waterplane, a correction is necessary. 

2nd, Find the Moment of Inertia of the Waterplaney relatively to 
a Transverse Axis passing through the Centre of the Waterplane. — 
Rule, Multiply the area of the waterplane by the square of its 
distance from the first ordinate. This product subtracted from 
the moment of inertia relatively to the first ordinate gives the 
moment of inertia relatively to the axis passing through the 
centre of gravity of the waterplane. 

By applying this rule to the figure at the beginning of Example 

20, we shall see that it agrees with S — . 



CALCULATIONS. 



293 



No. of 
Ord. 



1 
2 
3 



JOrds. 


S. M. 


* Products. 


Squares of 
Intervals. 


Moments. 


4-5 
4-5 
4-5 


1 

4 

1 


4-5 
18 
4-5 



1 

4 



18 
18 



Common interval cubed _ 3^ _ g 



36 
9 



Both halves 



324 
2 



Moment relatively to 1st ordinate 648 
Area of waterplane x (distance of centre of gravity from 1st 

ordinate)^ = (9 x 6) x 3^ = 486 

162 = 
Moment of inertia relatively to trausveroe axis passine through centre of 
WP. 

As alreaxly stated, the moment of inertia divided by the dis- 
placement in cubic feet gives the height of the longitudinal meta- 
centre above the centre of buoyancy. 

Calcvlationfor Longitudinal Metacentre above the Centre of Buoy- 
ancy. — As an example, the half ordinates of a ship's waterplane are, 
0, 4, 7, 9, 10, 8, 5, 2, 0. The common interval is 12 feet, the dis- 
placement, 150 tons. 



No. of 
Ord. 


iOrds. 


S.M. 


Prods. 


Leverages. 


Prods, of 
Moments. 


Levers. 


Prods, for 
M. of I. 


1 





1 

















2 


4 


4 


16 


1 


16 


1 


16 


3 


7 


2 


14 


2 


28 


2 


66 


4 


9 


4 


36 


3 


108 


8 


824 


5 


10 


2 


20 


4 


80 


4 


320 


6 


8 


4 


32 


5 


160 


5 


800 


7 


5 


2 


10 


6 


60 


6 


860 


8 


2 


4 


8 


7 


56 


7 


392 


9 





1 





8 





8 






i Longt. iuterval V = 



136 



508 
12 



(Com. int.)8 _ 
3 _ 



2268 
576 



544 
Both halves 2 

Area of waterplane 1088 



C.G of W.P from 

ord. 1.= 44*82 



1306868 

2 Both halves. 



2612786 Moment of 
inertia re- 
latively to 
ord. 1. 



The result at the foot of the fourth column is area of water- 
plane. Instead of multiplying the products obtained after using 



294 KNOW YOUR OWN SHIP. 

Simpson's Multipliers, by the square of the number of intervals in 
one operation, it is done in two operations, as shown in the fifth 
and seventh columns. This enables us to use the sixth column in 
order to ascertain the position of the centre of gravity of the 
waterplane, as shown in the calculation. 

Area of waterplane x square of the distance of C.G of water- 
plane from first ordinate = 1088 x (44*82)2 ^ 2185609. 

2612736 Moment of inertia relatively to ordinate 1. 
2185609 



150 tons X 35 = 6250)427127 M. ofl. about axis passing through C.G of W.P. 

81-35 feet = Height of longt. M.0 above O.B. 



Example 25. 

Alteration of THm. — The longitudinal metacentric height is 
cliiefly used in order to ascertain the alteration to trim caused by 
loaxling, discharging, or shifting weights or cargo on board a vessel. 
The principle upon which Trim calculations are worked is fully 
explained in Chapter VII., to which the reader should refer at this 
stage. A variety of examples are dealt with at the end of that 
chapter. 

The moment altering the trim 1 inch, when a vessel is floating at 
any particular draught, has been shown to be 

D X G M p ? = displacement 

:— — G M = metacentnc height. 

W L X 12 W L = length of waterplane. 

Suppose, in the previous example where the longitudinal meta- 
centre was found to be 81*35 feet above the centre of buoyancy, 
that a w^eight of 8 tons in the fore hold, and at a distance of 30 
feet forward of the centre of gravity of the waterplane, is dis- 
charged. What would be the alteration in trim ? 

The moment altering the trim is 8 x 30 = 240 foot tons. 

The "toDS per inch" is ^-^ = 2-59 tons. 
^ 420 

g 

The decrease in drautrht is therefore = 3 "08 inches. 

^ 2*59 

The moment to change trim 1" = 

150 X 82-35 G.M (supposing the C.G is found to be 1 foot below O.B) = 

96 X 12 
4117-5 



38-4 



= 10-72 



Change in trim = ^^ = 22 '38 inches. 
* 10-72 



CALCULATIONS. 295 

Suppose the vessel to have been floating upon even keel at a 
draught of 6 feet before the weight was discharged. By discharg- 
ing the 8-ton w^eight from forward, the vessel has changed trim 
iri9-inches at the stem, and Il*19-inches at the stem. 

Draught forward. Draught aft. 

6' 0" 6' 0" 

less 11-19 add 11-19 



m 



5'-0"-81 6' -11" -19 

The mean draught has decreased 3 08 3*08 

by 3-08" 

Draught after weight discharged 4'-9"-73 6'-8"ai aft. 



Example; 26. 

Alter attun of Trim caused by Damage to Fore Peaky owing to 
Collision. — As a further example of change of trim, suppose 
this vessel has a fore-peak watertight bulkheaxl, at a distance of 
15 feet from the stem, extending a considerable height above the 
waterline (the length from stem to stem being 96 feet). Let the 
draught be as before, 6 feet on even keel. Owing to collision, 
this fore peak is damaged, and water is admitted from the sea. 
A very important question in such a case is " What will be the 
change in trim after the ship has again come to rest ] " 

First of all, it is clear, that, owing to the loss of buoyancy in 
the fore peak, the mean draught must have increased. Immedi- 
ately the fore peak is perforated, and free communication estab- 
lished with the water outside, the waterplane of the ship termin- 
ates at the after side of the fore-peak bulkhead, the part before 
the bulkhead providing neither buoyancy nor moment of inertia 
of waterplane. 

The loss of buoyancy in the fore peak must be compensated for 
by the vessel increasing in draught, and obtaining the amount 
lost from the reserve buoyancy abaft the peak bulkheaxl. 

The amount of lost buoyancy must be found. This is, of 
course, the voliunc of the fore peak below the 6-feet draught level. 
Though there may be considerable space in the fore peak above 
the 6-feet level, this never afforded buoyancy, being entirely 
reserve buoyancy. Now that the peak is damaged, it is no longer 
reserve buoyancy, so that the buoyancy to be dealt with is simply 
that below the 6-feet level. This volume could easily be calcu- 
lated by Simpson's Rules, as shown previously for displacement, 
in fact, it is simply a calculation of the displacement of the fore 
peak. Let the capacity be 210 cubic feet or 6 tons. The centre 
of gravity of the waterplane between the stem post and the 



296 KNOW YOUR OWN SHIP. 

fore-peak bulkheaxl has next to be found, and also the centre of 
buoyancy of the fore-peak displacement. Then axld together the 
distance of the centre of gravity of the waterplane from the fore- 
peak bulkhead, say, 38 feet, and the distance of the centre of 
buoyancy of the fore peak from the bulkheaxl, say, 5 feet. The 
simi 43 is the leverage used in ascertaining the moment altering 
trim. 

Moment to alter trim = 6 x 43 = 258 foot tons. 

The length of the waterplane is now 96 - 15 = 81 feet. 

The area of the waterplane will be less, let it be, say, 1030 
square feet. 

The shortening of the length of the waterplane and the reduc- 
tion of its area will have reduced the longitudinal metacentric 
height. Let it be now 74 feet. 

The moment to alter trim 1 inch will be : — 

150_x_74 J 3700 _ -, ..^ 
81 X 12 324 

258 
a xTun - 

intact waterplane. 

The ** tons per inch " - 12?2 = 2-46 
^ 420 

/» 

The increase in mean drau(;ht = = 2*45 inches. 

® 2 '45 

The new draught will be : — 



258 

Total change in trim •—— = 22*6 inches = 11*3 inches, at each end of 
® 11 -^2 



Aft. 


Forward. 


6' 0'' 


6' 0" 


2-46 


2-45 



6 2*45 6 2-45 

-11-3 + 11-3 



5 3-15 7 1-75 

But the draught 7 feet If inches forward is at the collision 
bulkhead, and we require the draught at the stem 15 feet 
forward. 

The length from G 6 of waterplane to stem is 38 + 15 = 53 feet 

11-3" X 63 ,c T • V 
^ = 16 •/ inches. 

do 

6' 2-46" 
1 3-7 



The draught at stem will be 7' - 6 -15" 



CALCULATIOKS. 



297 



Example 27. 

To find the area of a wedge-shaped figure, such as shown by 
A B G in the adjoining figure, 
which may be taken to re- 
present one of the wedges of 
immersion or emersion of a 
rolling vessel, B C being a 
plain curve. Let the whole 
angle at A = 40 degrees. 
Divide the angle at A into 
a number of equal angular 
intervals, so that the whole 
number of radii may be suit- 
able for the application of one 5 
of Simpson's Rules. 

Rule. — Measure the length of 
each of the radii, and find their ^ 
half squares. Treat these half 
squares as if they were ordi- 
nates of a curve, by the applica- 
tion of Simpson's Rules. If 
the first of Simpson's Rules be 

applied, then the sum of the half squares will require to be 
multiplied by \ of the common angular interval, which must be 
taken in circular measure. 

Note, — Circular measure for 1 degree is '01745. 

The calculation would be arranged as follows : — 




No. of 
Radius. 


Radii 


Squares of 
Radii. 


S. M. 


Products. 


1 
2 
3 
4 
5 


20-0 
20-5 
21-0 
21-5 
22-0 


400-0 
420-2 
441-0 
462-2 
484-0 


1 
4 
2 
4 

1 


400«0 
1680-8 

882-0 
1848-8 

484-0 



Divide by 2 for half sqs. 2)5295-6 

1745 2647-8 
^^ = -0581 



i of circular measure for 10** = 



Area 153*8 



296 KNOW YOUR OWN SHIP. 



Example 28. 

To Find the Vdluine of a Wedge of Immersion or Emersion, — 
Suppose that the figure in the previous example haxl been one 
of the sections in a wedge of immersion 100 feet long, then, by 
dividing the length of the wedge into a suitable number of equal 
intervals, and finding the area of the sections at each of these 
intervals, and treating these areas as though they were ordinates 
of a new curve by the application of one of Simpson's Exiles, the 
volimie of the whole wedge would be ascertained. 

Example 29. 

To Find the Longitudinal Centre of Gravity of a Wedge, such as 
that jv^t dealt with. — Rule. Multiply the area of each sectional 
area by its distance from one extremity (call it x) of the wedge. 
Treat the products as though they were ordinates of a new curve 
of the same length as the wedge (100 feet), by the application of 
one of Simpson's Rules ; the result so found will be the moment 
of the wedge relatively to the extremity x. This moment, divided 
by the voliune of the wedge, will give the longitudinal distance 
of the centre of gravity from the extremity x. 

Example 30. 

To Find the Perpendicular Distance of the Centre of Gh^avity of 
the For fi- Mentioned Wedge (see fig. in Example 27), relatively to the 
Longitudinal Plane ZAS, which is perpendicular to tJie Radius A O. 
— Rule. Divide the wedge into a number of longitudinal planes, 
radiating from the edge A a at equi-angular intervals. Find the 
moment of inertia of each of these longitudinal planes (5 in 
number, see the fig.) relatively to A a, as explained in Example 
20, page 290. Multiply each of these moments of inertia by the 
cosines of the angles (see page 268) made by their respective 
planes with the plane A C, and apply to these results the multi- 
pliers for Simpson's First Rule. The sum of these products must 
be multiplied by J of the common interval (using circular meas- 
ure). The result is the moment of the wedge relatively to the 
plane ZAS. This moment, divided by the volume of the wedge, 
gives the distance of the centre of gravity of the wedge from the 
longitudinal plane Z A S.- 

When finding the centre of gravity of the wedge, as described 
in this example, the volimie of the wedge is usually found as 
follows (example 31) : — 



CAtOUtAlJIONS. 



ESAHFLB 31. 

To Find Volume of Wedge of Immersion or Emernvm. — The wedge, 
us hais been explained, is divided into 5 longitudinal planes radiat- 
ing from A a, whicli planes have already been divided into a number 
of equal intervals longitudinally, suitable for the application of 
Simpson's Multipliere (this has been done in order to find the 
moment of inertia in the previous example). Measure the 
ordiuates, and compute their half squares. Treat these half 
squares as though they were ordinates of a new curve by the 
application of Simpson's Multipliers, and find the hypothetical 
area in the usual way. The results thus obtained are moments 
for eath of the longitudinal planes. 

Use now these moments of planes as though they were ordinates 
of another new curve by the application of Simpson's Multipliers. 
The sum of products thus obtained, multiplied by J of the angular 
interval, gives the volume of the wedge which ought to agree 
with the result obtained by the method previously described in 
Example 28, where the transverse sections were dealt with. 

ESAUPLE 32. 

Calculationfor Finding t}ie Position of Die Centre of Effort Itela- 
tivelij to tJie Centre of Lateral Resistance. — In order to work out an 
actual example, the Three-masted Schooner-rigged Vessel, page 
213, is used. The sails are nnmbeied as shown upon the diagram. 
The steps in the process of the calculation are fully explained in 
Chapter VI. (Section VII.). 







Diatancsfl of 




Height of 








Centres of Sails 


Moments, 


Centre of 




Ko. of 
Soil. 


ai.Te't. 


from Centre of 


Sails above 
CentcB of 
Lateral 


Vertical 
Moments. 






Before. 
Feet. 


Abaft 
Feet. 


Befoi'e. 


Abiift. 


Feet. 




1 


480 


45 




21,600 




25 


12,000 


2 


560 


35 




19,600 




24 


13,440 


3 


580 


30 




17,400 




22 


12,790 


1 


1000 


1-2 




12,000 




28 


28.000 




aoo 


15 




4,500 




50 


16,000 


6 


1100 




S 




8,300 


28 


30,800 


7 


350 




4 




1,400 


51 


17,850 




lEOO 




30 




45.000 


26 


39,000 


9 


810 




26 




8,500 


60 


17,000 



Sum 76,100 08,700 



300 KNOW YOUB OWN SHIP. 

As the moments before the centre of lateral resistance prepon- 
derate, it is evident that the centre of effort lies forward of the 
centre of lateral resistance, and the distance is : — 

75100 -63700^ 1.83 f,3t. 
6210 

The height of the centre of effort above the centre of lateral 
resistance is : — 

185860 ^29-92 feet. 
6210 



CALCULATIONS. 



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304 



KNOW TOUR OWN SHIP. 



WETTED SURFACE AND SHELL DISPLACEMENT. 



Up to 4' 0" Waterline. 



o > 


Half 


CO. 


Girths. 


1 


4-1 


2 


4-5 


3 


7-2 


4 


101 


5 


11-8 


6 


12-9 


7 


13-2 


8 


12-9 


9 


11-9 


10 


10-0 


11 


7-9 


12 


6-2 


13 


0-0 






Pro- 
ducts. 



1 
4 
2 
4 
2 
4 
2 
4 
2 
4 
2 
4 
1 



4-1 
18-0 
14-4 
40-4 
23-6 
51-6 
26-4 
51-6 
23-8 
40-0 
15-8 
20-8 

0-0 



330-5 
J longt. interval 4 

1322 
Both sides 2 

Total Area of" 
Immersed 
Surface, which 
is the Wetted 
Surface, 



2644 
' sq. ft. 



Up to 8' 0" WaterHne. 



o • 



1 

2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
13 



Half 
Girths. 

8-0 

9-4 

12-3 

14-7 

16-1 

17-0 

17-3 

17-0 

16-1 

14-3 

12-2 

9-4 

4-0 






1 

4 
2 
4 
2 
4 
2 
4 
2 
4 
2 
4 
1 



Pro- 
ducts. 



8-0 
37-6 
24-6 
58-8 
32-2 
68-0 
34-6 
68-0 
32-2 
57-2 
24-4 
37-6 

4-0 



487-2 
4 

1948-8 
2^ 

Area 3897 6 



Up to 12' 0" Waterline. 



o . 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 



Half 


• 


Girths. 


1 


12-5 


15-1 


4 


16-7 


2 


18-8 


4 


20-1 


2 


21-0 


4 


21-3 


2 


21-0 


4 


20-1 


2 


18-4 


4 


16-2 


2 


13-6 


4 


8-0 


1 



Pro- 
ducts. 



12-5 
60-4 
88-4 
76-2 
40-2 
84-0 
42-6 
84 
40-2 
78-6 
32-4 
54-0 
8-0 



640-5 
^ 

2562 
2 

Area 5124 



Let the average thickness of shell plating up to the load line be 8/20. 

I 
As the strakes of plating are alternately in and out the average thick 



ness from the frames to the outside of the plating will be : — 



2644 

1 

2644 

20 
3897 

20 
5124 

20 



8 + 4 
20 



— of an inch. 



12 
20 






1 
12 



20 



of a foot. 



X ;rr = 



1 

20 
35 



2644 
20 



cubic feet displacement. 



35 = 5-5 



-r 35 = 7-3 



3 '7 tons displacement at the 4 ft. waterline. 

8 ft 



}) 



)) 



)) 



}) 



jy 



ff 



12 ft. 



tt 



it 



Notes on Wetted Surface Calculation.— The half girths of the frames, 
measured from the top of the keel to the height of the particular waterlines, up 
to which the areas are required, are taken at each section. These are Isreatea 
as the ordinates of a new curve, and the area found, by the application of 
one of Simpson's Rules, in the usual way. The area of the immersed keel, 
stem, and stem frame, may be added to this. 

Shell DisplacemerU Calculation.— The area of the immersed surface mnlti- 
plied by the average thickness, from the frames to the outside of the plating, 
gives the volume of displacement. 



CALCULATIONS. 



305 



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306 



KNOW TOUB OWN SHIP. 



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CALCULATIONS. 



307 



DISPLACEMENT CALCULATION. 

2nd Method of An^angement, 



No. of 


Top of 


I'O" 


2'0" 


3' 0" 4' 0" 1 


6'r 


8'0" 


lO'O" 


12' 0" 




Oi-d. 


Keel. 


W.L. 


W.L. 


W.L. 


W.L. 


W.L. 


W.L. 


W.L. 


W.L. 


\ 


2 


•12 


•66 


108 


1-42 


1-89 


3-00 


4-60 


6 •78 


8-71 


4 


•12 


4-46 


6-60 


7-92 


8-80 


10-14 


10*86 


11-26 


11-40 




r> 


•12 


7-80 


9-90 


10-87 


m-44 


11-90 


11-98 


11-96 


11*90 




8 


•12 


7-92 


9 90 


10-80 


J. 11-25 


11-71 


11*86 


11*90 


11-86 




10 


-12 


6-06 


6 86 


7-86 


8-48 


9-34 


9-86 


10-28 


10-60 




12 


-00 


136 


2-23 


2-80 


317 


3-80 


4-24 


4^66 


4*98 




a 


•60 


28-22 


36-6fi 


41-67 


45-03 


49-89 


63-37 


66*77 


69-34 


2a 


1-20 


66-44 


7312 


83-34 


90 06 


99-78 


106-74 


118*64 


118 68 


(01 


•06 


•06 


-06 


•06 


-06 


•06 


-07 


-30 


1-00 




3 


•12 


216 


3-66 


4-76 


6-70 


7 40 


8-80 


9-88 


10-65 




5 


•12 


6-70 


8-65 


9-80 


10-61 


11-36 


11-66 


11-76 


11-76 




7 


•12 


8-40 


10-22 


11-06 


11-61 


11-90 


12*00 


12*00 


11*98 




9 -12 


7-00 


8-70 


9-74 


10-38 


11-02 


11-81 


11*46 


11*61 




11 -12 


3-36 


4-72 


6 64 


6-06 


6-93 


7*60 


910 


8*46 


Sums of 


(^13 -00 


0-00 


000 


0-00 


0-00 


•10 


•16 


-18 


•22 


Func- 
tions 
=of Hori- 


1-86 


84-11 


109-12 


124-29 


134-27 


148-66 


168-82 


168-21 


174*26 


Simpson's ) , 
^Multl- )■ * 
pliers ) 


1 


i 


1 












zontal i 


2 


\ 


2 


i 


Areas. 


•46 84-11 


27-28 


124-29 33-66 


29710 7916 836*42 87-12 


• 


84-11 


124*29 


297-10 386-42 






•46 


27-28 


67-13 79-16 




Sum of Multiples \ 
of Functions / 






111-86 


• 


296-98 


■ 


740^87 




111-85 


296-98 


74087 


1248^07 


Multiplier for Displacem 


ent •60i 


J 


•608 


( 


•608 


t 


-608 




1 


89480 


237684 


692296 


994466 




671100 


1781880 


4442220 7468420 








Tons C 


;8 -00480 


180-66884 


460*14496 766*78666 



Shell displacement to add. See page 804. 

CALCULATION FOR "TONS PER INCH IMMERSION." 



2* 0" 
W.L, 


4'0" 
W.L. 


8'0" 
W.L. 


12' 0" 
W.L. 


rSum of Functions 
= X of Horizontal 
i. ^ Areas. 

Areas of Waterlines 


« « ,« 109-12 
2x2x12 _ jg 


184-27 
16 


168-82 
16 


174*25 
16 


4-20)1746-92 


420)2148-82 


420)268812 


420)2788 


Tons per Inch 4-16 


6-11 


6*03 


6-63 



Notes on Displacement CaleultUicn, 2nd Method. — This calculation involves somewliat less 
labour than the first method. It is simply a method of using Simpson's ^ Multipliers through- 
out All the even ordinates are put in the top column, and the sum of them, a, to multiplied by 
2, and placed in the 2a line. In the column below, the odd ordinates are placed together with 
half of the endmost ordinates, and these are added together, including the 2a line. By tills pro- 
cess we have simply used, 4, 2, 1, 2 and so on, as Simpson's Multipliers, instead of 1, 4, 2, 4, etc. 
The sum of these horizontal functions are treated by Simpson's | Multipliers, and ttie displace- 
ments found as before. It will be noted that the multiplier for displacement is *608, this being 
•162 x '2 (for horizontal ^ Simpson's Multipliers) x 2 (for vertical i Simpson's MultipUers) s *608. 

Tons per Inch.— The area of each parttcnlar wateirplane ia obtained by multiplying the sum 
of the functions of the horizontal half areas by 2 for ^ Simpson's Multipliers, by 3 for the 
other side, and by | of the longitudinal intervals 

2x2x12 ^^^ 



308 



KNOW TOUR OWN SHIP. 



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OALOITLATIOKB. 



CALCULATION FOR LONGITUDINAL CENTRES 
OF BUOYANCY. 

2nd Method of Arrangertient. 





II 


|i 


W.L. 


2'0' 


W.L. 


K 


fl-O" 


wT. 


K 


W.L. 


= 1011'. 


10 




2 

o'Stt 


i 




HB 


.i| 


B11» 
41flO 


4-BO 
46-64 


8s-ao 


81-91 


■ 




8-00 


177-74 


Mfi-sa 


846-87 


STau 


S00-7S 


BIS-OT 


3M-8S 


884-64 


is. 

IS 


10 


■48 

J 


3Sfi'4S 
0-00 

mm 
00 


O-M 

o-oc 


O'OO 


i 


8816 


630 -H 

W-48 
16 -00 
180 


0-00 
M-00 


869 '28 
0-00 

84-60 






1 


SISSH 


67 -7* 


7Bl-fl« 


.,.,. 


891-80 


835-06 


977-M 


* 


2-40 636'S8 ISf-eS 
LodgittuUnBL Inlervol, = 12 


7S1'BS aoi-M 
761-68 

«9e-si 

3M-98H«30-7* 


408-43 
1830-74 

7M87)4*90-Si 

B-OS 

n. 


lSM-44 4M'g8 
1243-07)7406-68 

(t. 


PIKT5. 



Longitudinal Oentrt qf Svo^ont^.— Id this cdcnUtion, the ordinates (aee 
Dieplscement Sheet) for the varions waterplanes are maltiplied by their 
respective leverageB (intervala) from the flret ordinate, and the moments so 
obtained are treated b; Simpson's HultiplieTS. In the abore calcahitlDi], 
the centre of buoyancy is worked for four separate dranghta, giving four 
separate results. 

The sums of moments are next treated by Simpson's Haltipliers, and the 
new sum is divided by the "sum of multiples of fnnctioDs" (from the 
Displacement Sheet). This result^ multiplied by the common interval, gives 
the position of the longitudinal centre of bnoyancy ratatiTely to the first 



310 



KNOW TOUR OWN SHIP. 



CALCULATION FOR HEIGHTS OF TRANSVERSE META- 
CENTRES ABOVE CENTRES OF BUOYANCY. 

2nd Method of Arrangement, 



No. of 
Ord. 



2 
4 
6 
8 
10 
12 



a 



2a 

5 

7 

9 

11 

(J) 13 



2^ 0" W.L. 



Cubes of 
^ Ordinates. 



4' 0" W.L. 



Cubes of 
i^ Ordinates. 



8' 0" W.L. 



Cubes of 
^ Ordinates. 



12' r W.L. 



Cubes of 
i Ordinates. 



1-25 
287*49 
970-29 
970-29 
321*41 
11*08 



2561-81 



5123*62 

0*00 

48-62 

647*21 

1067*46 

658*50 

105*15 

0*00 



Functions of Cubes, 7650*56 

5-33 



2295168 
2295168 
3825280 



2380*)40777*4848 



M.C. above C,B.=17*13ft. 



6*75 

681*47 

1497*19 

1423*82 

609*80 

31*85 



4250*88 



8501*76 

0*00 

185-19 

1160*93 

1524*84 

1118*38 

221*44 

0*00 



12712*64 
5-33 



8813762 
3813762 
6356270 

?)67757-8382 

o> 



CO 



97*33 

1277*28 

1719-37 

1664*00 

955*67 

76*22 



5789-87 



11579*74 

0*00 

681*47 

1581*16 

1728 00 

1446*78 

438*97 

0-01 



17466*08 
5*38 



* 



6236824 
6236824 
8728040 



10*72ft. 2 



)93040*9064 
5 6*90ft. 



660-77 
1481*54 
1685-15 
1664*00 
1157-62 

123-60 



6772-58 



13546-16 

4-00 

1207*94 

1622*23 

1719*87 

1524-84 

605-49 

•04 



20229*07 
6*33 



6068721 
6068721 
10114636 



94 



)107820*9431 



4*07ft 



Mull^lier for 
Moment of 
Inertia. 



Moment 
Inertia. 



of 



* rs displacement in cubic feet 



With the previous explanations the only point in this calculation 
needing comment is the multiplier 5*33. 



12x2x2 
3x3 



= 5-33. 



Where 12 is the longitudinal interval 

2 is for half Simpson's Multipliers. 

2 is for both halves of waterplane. 

3 is for J of cubes. 

3 is for I of longitudinal interval. 



OALCDTiATIOtra. 



a -es 



1 Is 

5 fl i 

iitii 



ri 



m 









;:s^|?3s:s?$3^^ 



^i 3 



■ -I 

I 9 



21" 1 



312 



KNOW TOUR OWN SHIP. 



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CALCULATIONS. 



313 



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314 



KNOW TOUR OWN SHIP. 



By means of the results given in the foregoing calculations, 
curves may be constructed, see figs. 138 and 139 as described 
and illustrated in the earlier chapters of this book, by which 
means any of the quantities or distances may be ascertained for 
any intermediate draught or waterline. 

Care should be taken in noting that, while the draughts are 
measured from the bottom of the keel, the calculations have been 
for waterlines measured from the top of the keel, and need to be 
set off accordingly in constructing the curves. When a vessel 
trims by the head or the stem, the mean draught is that worked 
to, in taking any particulars from the curves 




Fig. 138.— Curves of Displacement— Tons per Inch Immkesion — 
Longitudinal Centres of Buoyancy set off from the Aft 
Side of the After Stern Post. 

Note. — 100 on the horizontal scale of tons equals 1 ton for the tons per 
inch immersion, and 10 feet for the longitudinal centres of buoyancy. 

Stability Calculations. — Fig. 140 shows our vessel keeled 



CALCULATIONS. 



315 



to an angle of 14**, at which angle the stability is computed in the 
stability calculation, page 320. 

In fig. 140, V = the volume of the wedge of immersion, or, 
the wedge of emersion. 

BR is what the righting arm of stability would be if the centre of grayity 
coincided with the centre of buoyancy in the upright condition. It is per- 
pendicular to the vertical line through B'. 

BR may therefore be called the lever of stability produced by design or 
form. It is usually called the lever of statical surface stability. 




Fig. 139.— Curves op Vbbtical Centres of Buoyancy— Transverse 
Metacentrks — Longitudinal Metacentres (note, 3 feet on the 
Vertical Scale Reprbsbntb 100 feet). 



G is the centre of gravity of the ship, its position being governed by the 
loading and position of weights carried. 
The lever of statical stability is therefore : — 

BR - BC - GZ BC - BG X .sme of angle of ir. 



316 



KNOW TOUR OWN SHIP. 



The moment of statical surface stability is BR x displacement in tons. 

The moment of statical stability is GZ x D (displacement in tons). 

gh and ^h' are perpendicular to W'L'. 

B' is the position of the centre of buoyancy at 14° of inclination. 

g^ g' are the centres of gravity of the wedges of immersion and emersion. 



BB 



,_Vxgr/ 
D 



BR = 



Yxhh' 
D 



G Z = -1-^ - BG. xsine of 14° 



— jT— - (BG. sine of 14°) | 




Fig. 140. 



Fig. 141 shows the sections of our vessel prepared for the 
stability calculation. The calculation is divided into two parts, 
the first being of a preliminary nature in order to obtain results 
which are transferred to the combination table in the second part. 

From the stability sections, the ordinates are measured for 
the upright, and the two inclined, waterplanes, for both the 
immersed and emerged wedges, and inserted in their proper 
columns in the preliminary tables. 



CALCULATIONS. 317 

The three results obtained in the preliminary tables almost 
explain themselves, after the examples worked in Section I. of 
this chapter. 

(1) By treating the ordinates by Simpson's Multipliers, the total area of the 
new horizontal waterplane is obtained, W L' (fig. 140), — the immersed and 
emerged sides being added together. This is only necessary for the third 
waterplane in the calculation. See Example 10. Section 1 of this chapter. 

(2) By treating the half squares of ordinates by Simpson's Multipliers, it 
is found on which side of the inclined waterplane there is a preponderance 
of moment. In this case, the immersed is the greater. The centre of 
gravit}*^ of the waterplane, therefore, lies towards this side. By subtracting 
the emerged side from the immersed, and dividing by 2 for ^ squares, and 
multiplying by ^ of the longitudinal interval, the preponderating moment is 
ascertained. This, divided by the area of the same inclined waterplane, 
gives the distance the centre of gravity is out from the longitudinal middle 
line of the waterplane on the immersed side. See Example 17. 

It will now be seen that the area was necessary in order to find the transverse 
centre of gravity of the whole inclined waterplane. 

(3) By cubing the } ordinates of the three planes, and ultimately taking 
one-third of them, we obtain the moment of inertia which is necessary in 
order to find the moments of the wedges. See example 30. 

In fig. 141 the wedges of immersion and emersion have been 
drawn as though the waterplanes for all angles of inclination 
intersected at the original fore and aft centre line of the upright 
waterplane. In reality, these waterplanes do not, at least for 
considerable inclinations, for it is well known to the reader that the 
volume of the wedge of immersion so obtained, would in all 
probability, differ from the volume of the wedge of emersion. So 
a correction becomes necessary in order to arrive at an accurate 
result. If the volume of the wedge of immersion be larger than 
that of the wedge of emersion, it is clear that the vessel is drawing 
more water in the diagram than she does in reality. By dividing 
the difference in volume of the two wedges as calculated, by the 
area of the waterplane, the thickness of the correcting layer to be 
deducted from the draught is ascertained. Had the immersed 
wedge been less than the emerged, the difference in voliune of the 
two wedges divided by the area of the waterplane, would give the 
thickness of the layer to be added to the draught. In the com- 
bination table, the volume of the immersed and emerged wedges 
are calculated as explained in Example 31, and the thickness of 
the correcting layer is obtained. 

In our vessel we see that the volume of the wedge of immersion 
exceeds that of the wedge of emersion by 89*75 cubic feet, and the 
thickness of the correcting layer is '03 feet. And as the centre 
of gravity of the inclined waterplane which represents the centre 
of gravity of the correcting layer is '25 feet (see preliminary table) 
towards the immersed side, the moment of the wedges is in excess. 



318 KNOW TOUR OWN SHIP. 

and the moment of the layer must be deducted from the moment of 
the wedges. Had the centre of gravity of this layer lain towards 
the opposite side, its moment would have had to be added. 

The last operation in the combination table is to find the 
moment of the wedges. This process has been fully explained in 
Example 30. The sums of the fimctions of the cubes of the 
ordinates for the waterplanes of both wedges, are transferred from 
the preliminary tables. These functions are treated by Simpson's 
Multipliers, and also by the cosines of the angles of inclination, 
obtaining " functions of cubes for moments of wedges." The sum 
of these functions for moments is divided by 3, as J of cubes of 
ordinates is required for moment of inertia of waterplanes. The 
result is multiplied by ^ of the angular interval, and this by J of 
the longitudinal interval giving moment of the wedges relatively 
to a plane passing through xl^y perpendicular to W, N, L' (see 
fig. 140). From the moment of wedges is subtracted the correct- 
ing moment for the layer, and the remainder divided by the 
displacement gives the distance BR (fig. 140) produced by the 
transference of the wedge WNW to L'NL, a distance hh\ 
To obtain the righting lever GZ, subtract BC from BR 
(BC = BG multiplied by the sine of the angle BGC, which 
is 14°). 

G Z X displacement = Righting moment in foot tons. 

As a check upon the G Z, when calculated for small angles of 
inclination (before the deck edge is immersed), not exceeding 10° 
or 15^ 

G M X Sine of angle = GZ. 

2 feet X '2419 =- 'dSSS which is approximately correct. 

Note, — The metacentre was found to be 4*07 feet above the centre of 
buoyancy and the metacentric height was assumed to be 2 feet. 

In order to construct a curve of stability a succession of calcu- 
lations, identical to that we have just described, would have to be 
made for the vessel inclined to a succession of angles of inclination 
in order to find the G Z's at each inclination. 



CALCDLATIONB. 




FjG, 141. — SSCTIONH FOK CALCULATION OF STATICAL STABILITY. 



320 



KNOW YOUR OWN SHIP. 



CALCULATION FOR THE STABILITY OF A VEg 

See fig. 

PSELIMIl 

Up 



Immersed Wedge. 


No. of 


Ordinates. 


Multi- 


Functions of 


Squares of 


Multi- 


Functions of 


Cubes of 


Multi- 


• Functions ' 


Section. 


pliers. 


Ordinates. 


Ordinates. 


pliers. 


Squares. 


Ordinates. 


pliers. 


Cubes. 


1 


2-00 






4 00 


1 


4-00 


8-00 


1 


8-00 


2 


8-71 






75-86 


4 


303-44 


660-77 


4 


2643-08 


3 


10-65 






113-42 


2 


226-84 


1207-94 


2 


2415-88 


4 


11-40 






129-96 


4 


519-84 


1481-54 


4 


5926-16 


5 


11-75 






138-06 


2 


276-12 


1622-23 


2 


3244-46 


6 


11-90 






141-61 


4 


566-44 


1685-15 


4 


6740*60 


7 


11-98 






143-52 


2 


287-04 


1719-87 


2 


8438*74 


8 


11-85 






140-42 


4 


561-68 


1664-00 


4 


6656-00 


9 


11-51 






132-48 


2 


264*96 


1524-84 


2 


3049-68 


10 


10-50 






110-25 


4 


441-00 


1157-62 


4 


4630*48 


11 


8-46 






71-57 


3 


143-14 


605-49 


2 


1210-98 


12 


4-98 






24-80 


4 


99-20 


128-50 


4 


494-00 


13 


44 






•19 


1 


-19 


•08 


J 


-08 


3693-89 


40458*14 
3 


80916-28 For 




1 














wet 










Prblimii 








Waterplane inc 


Immersed Wedge. 


1 


2-4 






6-7 


1 


5-7 


13-8- 


1 


13*8 


2 


9-5 






90-2 


4 


360-8 


857-8 


4 


8429-2 


3 


11 -0 






121-0 


3 


2420 


1331-0 


2 


2662-0 


4 


11-6 






134-5 


4 


538-0 


1560-8 


4 


6243*3 


5 


11-8 






189-2 


2 


278-4 


16430 


2 


3286-0 


6 


120 






144-0 


4 


576-0 


1728-0 


4 


6913-0 


7 


120 






144-0 


2 


288-0 


17280 


2 


3456 


8 


11-9 






141-6 


4 


566-4 


1685-1 


4 


6740-4 


9 


11-6 






184-5 


2 


269-0 


1560-8 


3 


3131-6 


10 


10-7 






114-4 


4 


457-6 


1225-0 


4 


49000 


11 


8-7 






75-6 


2 


151-2 


658-5 


3 


1817 


12 


5-2 






27-0 


4 


108-0 


140-6 


4 


563-4 


13 


•4 






•1 


1 


-1 


•0 


1 


•0 


3841-2 


42648*6 ImiiK 




















wed 




















40197-0 Emm 




















iro^ 




















83840-6 Stun 




















botl 




















wed 



CALCULATIONS. 



321 



INCLINED TO AN ANGLE OF 14 DEGREES, 
for Drawings. 

Table I. 
Waterplane. 



Emerged Wedge. 



No. of 
Section. 



Ordinates. 



Miilti- Functions of 
pliers. Ordinates. 



Squares of 
Ordinates. 



Multi- 
pliers. 



Functions of 
Squares. 



Cubes of 
Ordinates. 



Multi- 
pliers. 



Sams as Imukbskd Wrdge. 



Functions of 
Cubes. 



Table II. 

to an angle of 7°. 



Emerged Wedge. 


1 

1-8 




3-2 


1 3-2 


6-8 


1 


5-8 


7-9 , 




62-4 


4 249-6 


4930 


4 


1972-0 


10-8 




106-0 


2 2120 


1092-7 


2 


2185-4 


11-4 1 




129-9 


4 519-6 


1481-5 


4 


5926-0 


11-9 






141-6 


2 283-2 


1685 1 


2 


3370-2 


12 1 






146-4 


4 585-6 


1771-5 


4 


7086-0 


121 




146-4 


2 292-8 


1771-5 


2 


35430 


120 






1440 


4 576-0 


1728-0 


4 


6912-0 


11-5 




132-2 


2 264-4 


1520-8 


2 


3041-6 


10-4 




108-1 


4 432-4 


1124-8 


4 


4499 2 


8-4 1 




70-5 


2 1410 


592-7. 


2 


1185-4 


4-9 






24-0 


4 96 


117-6 


4 


470-4 


•4 




•1 


1 1 


•0 


1 


•0 






3655-9 


40197-0 



1 

2 
3 
4 

5 

a 

7 
8 
9 
10 
11 
12 
13 



322 



KNOW YOUR OWN SHIP. 



CALCULATION FOR THE STABILITY OF A VESI 

PllELIMIN 

(Waterplane incli 



Immersed Wedge. 



No. of 
Section. 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 



Ordinates. 


Multi- 
pliers. 


31 


1 


10-3 


4 


11-4 


2 


11-8 


4 


12-0 


2 


120 


4 


12-2 


2 


12-2 


4 


lit) 


2 


111 


4 


9-2 


2 


6'4 


4 


•4 


1 



Functions of 
Ordinates. 



31 
41-2 
22-8 
47-2 
24-0 
48-0 
24-4 
48-8 
23-8 
44-4 
18-4 
21-6 
•4 



Squares of 
Ordinates. 



Multi- Functions of 
pliers. Squares. 



9-6 

1060 

129-9 

139-2 

144-0 

144-0 

148-8 

148-8 

141-6 

123-2 

84-6 

291 

•1 



1 
4 
2 
4 
2 
4 
2 
4 
2 
4 
2 
4 
1 



9-6 
424 
259-8 
556 8 
288-0 
676-0 
297-6 
696-2 
283-2 
492-8 
169-2 
116-4 
•1 



Cubes of 


Multi- 


Ordinates. 


pliers. 


29-7 


1 


1092-7 


4 


1481-6 


2 


1643-0 


4 


1728-0 


2 


17280 


4 


1816-8 


2 


1815-8 


4 


1686-1 


2 


1367-6 


4 


778-6 


2 


167-4 


4 


•0 


1 



Functions o: 
Cubes. 

29-7 
4370-8 
2963-0 
6672-0 
3466-0 
6912-0 
3631-6 
7263-2 
3370-2 
6470-4 
1567-2 
629-6 



Sum of functions / Immersed, 368 - 1 
of Ordinates, \ Emerged, 346-4 

Total, 714-5 
^ of longitudinal interval, . 4 

Total area of Waterplane, 2858-0 



Immersed side, . 4068-7 
Emerged side, . 3707-2 

Fori squares, . 2)361-6 difference 



46226 '7 Immeri 
wedg 

41419-2 Emergt 
wedg 



^ longitudinal interval, 



87644-9 Sum f o 
180-75 preponderance of i^ both 

squares on im-— i— i— wedgt 
mersed side. 



^^plane ^**®^' } 2858)723-00 moment. 



Centre of gravity = 



-25 of a foot towards immersed side. 



CALCULATIONS. 



323 



uINED TO AN ANGLE OF 14 DEGREES— con^inw^i. 



.E III. 

I angle of 14**.) 



Emerged "Wedge. 


of 


Ordinates. 


Multi- 


1 
Functions of , 


Squares of iMulti- 


Functions of 


Cubes of 


Multi- 


Functions of 


rion. 


pliers. 


Ordinates. 


Oi-dinates. j pliers. 


Squares. 


Ordinates. 


pliers. 


Cubes. 


1 


1-6 


1 


1-6 


2-5 


1 


2-5 


40 


1 


40 


2 


7-3 


4 


29-2 


63-2 


4 


212-8 


389-0 


4 


1666-0 


3 


100 


2 


20 


1000 


2 


200 


1000-0 


2 


2000-0 


4 


11-5 


4 


46 


132-2 


4 


528-8 


1620-8 


4 


6083-2 


5 


12 1 


2 


24-2 


146-4 


2 


292-8 


1771-5 


2 


3643-0 


6 


12 4 


4 


49-6 


153-7 


4 


614-8 


1906-6 


4 


7626-4 


7 


12-4 


2 


24-8 


153-7 


2 


307-4 


1906-6 


2 


8813-2 


8 


12-2 


4 


48-8 


148-8 


4 


695-2 


1815-8 


4 


7263-2 


9 


11-8 


2 


23-6 


139-2 


2 


278-4 


1643 


2 


8286-0 


10 


10-5 


4 


42-0 


110-2 


4 


440-8 


1167-6 


4 


4880-4 


11 


8-3 


2 


16-6 


68-8 


2 


137-6 


671-7 


2 


1143-4 


12 


4-9 


4 


19-6 


24-0 


4 


96-0 


117-6 


4 


470-4 


13 


•4 


1 


•4 


•1 


1 


-1 


•0 


1 


•0 



346-4 



3707 2 



41419-2 



324 



KNOW YOUR OWN SHIP. 



COMBINATION TABLE FOR STABILITY AT 14° INCLINATION. 



Immebsed Wedge. 


Emerged Wedge. 


Angles of 
Inclina- 
tion. 


Functions of 
Squares of 
Ordinates. 


Multi- 
pliers. 


Functions of Squares 

of Ordinates for 

Volume of Wedge. 


Functions of 
Squares of 
Ordinates. 


Multi- 
pliers. 


Functions of Squares 

of Oi-dlnates for 
Volume of Wedge. 


0' 

7" 
14- 


8693-8 
8841-2 
4068-7 


1 

4 

1 


3693-8 

15364-8 

4068-7 


3693-8 
3655-9 
3707-2 


1 
4 

1 


3693-8 

14628-6 

3707-2 



Immersed wedge, 
Emerged „ 

For half squares, 



i of angular Interval, 



23127-3 
22024-6 



22024-6 



2) 1102-7 difference. 

551-35 preponderance of half squares in immersed 
wedge. 
•0407 



i of longitudln{^l interval, 

Excess In volume of immersed 
wedge, 



385945 
2205400 

22-439945 
4 



89-769780 



Correcting Layer. 

89-769 X -26 (centre of gravity of waterplane 
towards immersed side. See 
Preliminai-y Table III.). 
=22*439 Moment for Layer. 



Area of waterplane, 



2858)89-759 



'03 of a foot Thickness of Layer. 



Both Wedges, 



Angles of 

Inc ina- 

tion. 


Sums of Functions 

of Cubes of 

Ordinates. 


Multi- 
pliers. 


Products of Func- 
tions of Cubes. 


Cosines of 
Angles of In- 
clination. 


Functions of Cubes 

for Moments of 

Wedges. 


0° 

7- 

14" 


80916-28 
82840-60 
87644-90 


1 
4 

1 


80916-28 

331362-40 

87644-90 


•9702 

•9926 

1-0000 


78604*9 

328877*1 

87644*9 



i of cubes 

I of angular inclination, 

I of longitudinal interval, 

Moment of wedges, . 
(Subtract) Correction for layer, 

Disp. in cubic feet, . 



3)496026*9 

166008*9 
*0407 

6716*8 

4 

26863*2 
-22*4 



26462*8)26840*8 



BR=s 
BGxSine of Angle = 2*07 x *2419ss 

Righting Arm GZs 



1*01 
•60 



*606 



Righting Moment of Stability =GZx Displacement in Tons ='506x766*78^881 -66 foot tons. 
Righting Moment wlien inclined to an angle of 14* =381*66 foot tons. 



325 



APPENDIX A. • 



The Author desires, in conclusion, to call the attention of such of his 
readers as have some mathematical attainments to an able Paper, read 
before the Institute of Marine Engineers, on Jan. 12, 1892, by John A. 
Rowe, Esq., Surveyor to the Board of Trade.* From this Paper, which was 
kindly placed at his disposal, he has made the following extract, which 
will be found of much interest : — 

DYNAMIC STABILITY AND OSCILLATIONS AMONG WAVES. 

"Most of you are aware that in computing the rolling period of a ship — 
that is, the time in seconds she will take to roll from the vertical and back 
again — she is somehow or other regarded as a pendulum. This is a correct 
view to take of the matter if the siibject is approached in a proper direction. 
But many able men have been perplexed by what has appeared to be the 
contradiction between theory and practice. For instance, most of you are 
aware that the period T of a bob-pendulum in seconds is : 

T = 3-1416 X ^ /Length^in feet ^ g.^^^g ^ Jh ^ .554 ^ ^"j; 
V Gravity V 32 

L is the length of the pendulum in feet. 

In this formula it is clear that the x)eriod of a pendulum varies as the 
square root of its length. 

For the smooth water period of a ship the formula is somewhat different, 
and is as follows : — 

T = 3-1416 / Radius of Gyration squ ared _ .gg^ ^ f B?_ 
\/ Gravity x Metacentric Height \/ G M 

The radius of gyration and the metacentric height to be in feet. 

An examination of this formula reveals the fact that a vessel's rolling 
period varies directly as the radius of gyration, and inversely as the square 
root of the metacentric height. If G M be increased in length, the vessel's 
period will be shortened, and she will become a quicker roller than before. 
Bat practical men looking at the usual diagrams, have reasoned thus:^ 
* The length G M is the distance between tne vessel's point of oscillation 
and her centre of gravity. If there is any pendulum-like motion in the 
ship it is of necessity about G or M, at a length G M.' 

But the formula T = '554 x /-£i_ shows clearly enough that whatever 

be the equivalent pendulum length it is not G M but is something entirely 
different. The following fig. has been constructed by the writer in the hope 
of simplifying some points not generally understood. 

The vessel is shown upright on the wave-slope. In this position the 
force of buoyancy, which acts at right angles to the wave surface^ as it acts 
at right angles to the surface of smooth water, creates a righting arm G Z. 
This length in feet, multiplied by the ship's weight in tons, is what we 
have called the vessel's righting moment in foot-tons. In the position we 

* Now Chief Examiner of Bngineen to the Board of Trade. 



APPBNDIX. 



h&ve shown her, it iB obrious that this poner, usaallj regarded bb the 
power of recovery, Btarta the veaael rolling ; aod if, after ahe had acquired 




gurface to the sea she would roll through the angle G M on each Bide of 



APPENDIX, 327 

the vertical, and gradually extinguish the range of oscillation by the fluid 
resistance offered to the immersed portion of the hull. 

Again, if GO and MT be drawn at right angles to GM, and TO drawn 
parallel to G M, we obtain a parallelogram of forces, whose resultant M 
may be regarded as the buoyant force which equals the weight of the ship, 
and whose components are GM and MT. As GM is acting upward 
tlirough the vessel's centre line we may disregard it, and direct our atten- 
tion exclusively to the component M T, whose direction is shown by arrow, 
and whose amount is M x sine of the angle of inclination. 

Let the effective angle of the wave-slope be 9**, the vessel's weight 
10,000 tons, her metacentric height 6 feet. Find the turning moment about 
G, the vessel's centre of gravity. 

The component M T = M x sine of 9° = 10,000 tons x -156 = 1560 tons. 

This force of 1560 acts at the end of the lever G M = 6 feet ; therefore, 
the righting, or in this case, the turning moment 

= 1560 tons X 6 feet = 9360 foot-tons. 

But the righting moment is the weight of the ship multiplied by the 
righting arm. What is the product of these quantities ? 

Ft. Foot. 

G Z, the righting arm = G M x sine of 9° = 6 x -156 = '936. 

Tons'. Foot. 

Righting moment 10,000 x '936 = 9360 foot-tons. 

Both calculations declare the righting moment to be 9360 foot-tons. 

In other words, the weight of the ship into the righting arm G Z = the 
component MT into the metacentric height. If now we plot Y as the 
centre of gyration, we shall be able to realise the nature of the force 
tending to produce motion, and the character of the resistance offered to it. 

Let us for a moment suppose that G is a fixed point — the ship's fulcrum. 
Let us also regard the ship as a portion of a huge wheel (a p-^rtion of a fly- 
wheel) its radius of gyration being G Y. 

By an examination of the fig. it will be seen that the greater GM is 
(with a given horizontal force M T) the greater is the turning moment. 
And the smaller the radius of gyration G Y, the smaller will be the resist- 
ance and the quicker will be the motion of oscillation. 

To obtain great stability and quick motion, we must increase the leverage 
G M, and reduce the pendulum length G Y ; to obtain moderate stability, 
but a slow angular motion, and, tlierefore, a comfortable vessel at sea, and 
one offering a steady gun-platform, we must diminish the leverage G M and 
increase the length of G Y. 

With regard to GY, which is obtained by dividing the vessel's moment 
of inertia about G by the sum of the weights, and extracting the square 
root, it is evident that it can be of great length only in a large vessel. In 
a small vessel, GY can be increased by placing movable weights towards 
the bulwarks, but no such change as this will be sufficient to make the 
radius of gyration great enough to give rise to a slow rate of oscillation. 
An easy motion in small crafts may be obtained by shortening GM, but 
this may give rise to want of stability. Hence the difficulty of builders to 
ntake a perfect ship. They have to steer between Scyila and Charybdis. 
Worse still, they strive to please shipowners, who know but little of the 
difficulties of naval architecture ; and to please themselves, with the result 
that they sometimes please neither. . . . 

Wave action upon ships, stores wave energy in ships to an extent depending 
on their weight and length of righting arm ; and the manner of ascertaining 



328 APPENDIX. 

the amount of work put into the before-mentioned ship is as follows : — The 
force MT = 1560 tons, becomes nil when the vessel's deck is parallel to 
the wave-slope or to a smooth sea. Therefore the mean force acting to turn 

the ship at M about the centre G is — - = — -_ = 780 tons. This mewn 
^ 2 2 

force acts through the space M T = M G x tangent of the angle of inclina- 
tion = 6 feet X -158 = '948 foot. And 780 tons x -948 foot = 739*44 foot 
tons dynamic stability. . . . 

Storm-waves produce violent rolling in the largest of floating stiuctures, 
and these structures are occasionally brought to rest by a sudden and com- 
plete expenditure of their stored energy. And the greater the energy in 
the vessel — i.e., the heavier the ship, and the quicker the motion, the more 
tremendous is the blow she can inflict upon an approaching wave. But, 
unhappily, when the momentum of an ocean wave is not only resisted by 
a vessel's hull, but is increased by the dynamic energy of the ship, a climax 
occurs, the severity of the blow is manifested by the vessel ceasing to roll 
(her energy being expended), and by the wave bursting high above the 
decks and sweeping them from end to end. This condition of things, as 
about to happen, the writer wishes to convey in the rough sketch, by 
arrows, showing the direction of the ship's oscillation and the wave's 
advance. The fig. is not by any moans to scale." The projections E K on 
each side of the diagram are short lengths of troughs which, in Mr. Rowe's 
opinion, would prevent rolling. They are open ended, and the dimensions 
would vary with the weight of the ship and the metacentric height. 
They would probably render torpedo boats habitable in choppy seas and 
stormy weather.* — (Krom paper on "Stability and Motions of a Vessel 
among Waves,'* by John A. Rowe. Part ii., p. 10, et seq,) 



APPENDIX B. 

TEST QUESTIONS.! 

CHAPTER I. 

1. What is displacement? What is a displacement curvet Explain its 
construction and use. 

2. What is deadweight? What is a deadweight scale, and how is it 
constructed ? ^ 

3. What is meant by " tons per inch " immersion ? Give and explain the 
rule for " tons per inch" immersion. 

4. Explain how a curve of "tons per inch" immersion is constructed, 
and show clearly its use. 

5. What is a coefficient of displacement ? State approximately the co- 
efficient for an average cargo steamer, and a fine passenger steamer. 

6. What is the weight of 1 cubic foot of salt water and 1 cubic foot of 
fresh water ? How many cubic feet of salt water, and also of fresh water, are 
there in 1 ton ? 

7. Find the displacement of a box ship floating light in sea water at a 

* By instantly exhausting the energy derived from each wave. These troughs would 
prevent the accumulation of energy and therefore limit the effect of wave action to that 
due to the passing of one wave only under the ship's bottom. 

t Many of these questions are taken from Science and Art Examination Papers. 



APPENDIX. 329 

draught of 5 feet forward and 6 feet aft. The length is 100 feet ; the 
breadth 20 feet (use mean draught). Ans, 314 '2 tons. 

8. When loaded, the box ship in the previous question draws 12 feet of 
water fore and aft. What is the dead weignt ? ^ris. 371*5 tons. 

9. A ship of 1000 tons displacement, loaded, is floating in sea water. 
What will be the change in draught in passing into river water! The 
** tons per inch " at the load line is 9. Aiis. Draught increases 1 '7 inches. 

10. A steamer on a voyage burns 200 tons of coal. The " tons per inch " 
is 24. What is the approximate change in draught! Ans, Draught de- 
creases 8*3 inches. 

11. A vessel is 200 feet long, 30 feet broad, and of 16 feet depth to top of 
weather deck at amidships. The freeboard is, say, 2 feet, and the coefficient 
of fineness '65. What is her displacement in salt water? Atis, 1560 tons. 



CHAPTER II. 

12. What is meant by saying that a vessel has a righting or a capsizing 
moment ? 

13. Define the term " centre of gravity." 

14. A ship has a displacement of 2000 tons when floating at a certain 
draught ; 100 tons are then placed on deck at a height of 9 feet above the 
centre of gravity of the ship as it was before the weight was placed on 
board. Find the alteration in the position of the centre of gravity. Ans, 
Centre of gravity is raised '42 foot. 

15. A ship, with a displacement of 2000 tons, has a weight of 100 tons, 
already on board on the centre of the upper deck, moved 8 feet to the port 
side. Find the distance the centre of gravity has shifted. Ans. '4 foot. 

16. The centre of gravity of a ship is 12 feet from the bottom of the keel. 
In this condition her displacement is 2500 tons. She is then loaded in the 
following manner : — 100 tons are placed 9 feet above the bottom of the keel, 
300 tons 14 feet, and 500 tons 12 feet. Find the new position of the centre 
of gravity from the bottom of the keel. Ans, 12*08 feet. 



CHAPTER III. 

17. What is meant by buoyancy, reserve buoyancy, centre of buoyancy ? 

18. How do water pressures act ? Which of them aff'ord support % 

19. What is meant by sheer ? and explain its use. 

20. Of what value are deck erections as regards buoyancy 1 

21. What is the vertical centre of buoyancy 1 also longitudinal centre of 
buoyancy % 

22. Show how curves of longitudinal and vertical centres of buoyancy 
are constructed. 

23. Supposing a ship's longitudinal centres of buoyancy to be in the 
middle of the length at every draught when floating on even keel, and she 
is loaded in the following manner : — 



10 tons are placed 30 feet forward of the centre of buoyancy 
120 .. 50 

500 
400 

15 
150 



II II II 

60 ,, ,, ,, 

70 feet aft ,, ,, 

60 ,, ,, ., 

25 ,, ,, ,, 



330 APPENDIX. 



Where would a weight of 200 tons need to be placed on board to bring her 
again on even keel ? Ans, 18*25 feet aft of the centre of buoyancy. 

24. Why does a ship increase in draught on a comparatively small com- 
partment being damaged below the water level, into which the sea enters ? 

25. What is meant by camber, and why is it given to a vessel ? State 
the rule for the minimum. 

26. A box ship is 100 feet long, 20 feet broad, and floats at 6 feet draught. 
Calculate the amount of upward water pressure in lbs. Ants, 768,000 lbs. 

CHAPTER IV. 

27. Enumerate in order of importance the principal strains to which a 
ship may be subject. 

28. State clearly what strains a ship may experience when floating light 
and in calm water. 

29. Show how strains may be decreased or enormously increased in the 
operation of loading. 

30. Describe the strains experienced by a ship among waves — fore and aft 
and athwartships. 

81. Explain the term " unequal distribution of weight and buoyancy.'* 

32. What is a compressive strain and a tensile strain ? 

33. Show in any graphic way how to combine and arrange ths material 
used in the construction of ships so as to give greatest resistance to bending. 

34. What kind of ships offer greatest resistance to longitudinal bending, 
and which offer least ? 

35. Where are the fore and after strains greatest ? Show why. 

36. What is the tendency of strains due to rolling motion ? 

37. What strains are supposed to be provided for in vessels built to the 
requirements of the recognised classifying societies? What strains may a 
vessel experience which such rules do not profess to cover? 



CHAPTER V. 

38. Enumerate the parts of a ship's structure known as transverse framing. 
What is the function of transverse framing ? 

39. Describe carefully and in detail how the parts which make up a com- 
plete transverse frame are connected with one another, and also the various 
forms of material which may be used. 

40. What is meant by compensation in ship construction ? Give illustra- 
tions. 

41. Give rules for beam knees. 

42. Which are the best beams to fit under iron or steel decks, and also 
under wooden decks ? Give illustrations. 

43. What depth must a ship be to require two tiers of beams, and also 
three tiers of beams ? 

44. How may the lowest of these tiers be dispensed with, and state 
clearly the compensation made for the loss ? 

45. What are web frames ? When and where are they fitted ? 

46. State which parts of the transverse framing specially resist the 
tendency to *' working," produced by rolling motion. 

47. Mention the parts comprising longitudinal framing. What is the 
function of longitudinal framing? 

48. What means are adopted to secure a good connection between the 
longitudinal and the transverse framing? 



APPENDIX. 331 

49. What is a bar keel ? How are the parts comprising this keel connected t 

50. What is a keelson and a stringer ? 

51. Sketch roughly the different forms of keels and centre keelsons, and 
state which (if any) combination is preferable. 

52. What is the garboard strake ? The sheer strake ? 

53. How is it that most of the material used in a ship's construction is 
reduced in thickness towards the ends? 

54. Describe any method adopted to compensate for cutting down a centre 
keelson or reducing a stringer plate in width. 

55. Describe what provision may be made to resist panting strains, and 
also strains from masts due to wind pressure. 

56. What are the special characteristics of a three-deck, a spar-decked, 
an awning-decked, and a quarter-decked vessel ? 

57. Why are bulkheads fitted? Show how they are connected to the 
shell plating. To what height are bulkheads carried? How is a recessed 
bulkhead made watertight? 

58. Show how a bulkhead is made watertight where a keelson or stringer 
passes through it. 

59. What is a rimer and a drift punch, and their use? Which is the 
best form of rivet, and why ? 

CHAPTER VI. 

60. Define the term *' stability." 

61. What are the two factors producing moment of stability ? 

62. What is the metacentre ? What is metacentric height ? 

63. What is meant by a righting moment of stabilit)' ? 

64. State the conditions under which a vessel will float in stable equi- 
librium. 

65. What is the condition of a ship which is said to be "stiff" or 
"tender"? 

66. Having given the metacentric height, how can the righting lever be 
found, and when is it unsafe to adopt this method ? 

67. Give the formula for finding the height of the metacentre above the 
centre of buoyancy. 

68. What features in the design are most important in influencing the 
height of metacentre ? 

69. How can stiffness be obtained ? 

70. What is a curve of stability, and how is it constructed ? 

71. It is usual for the metacentre to fall when the draught is increasing 
from light towards the load draught, but on approaching the load it is often 
found to rise again. What explanation can be given for this ? 

72. Describe clearly the steps of the operation for finding the metacentric 
height by experiment. 

73. Describe clearly the effect of beam, freeboard, and height of centre of 
gravity upon the maximum levers and range of stability. 

74. What is tumble home ? 

75. State the relation between metacentric height and transverse rolling 
motions in still water. 

76. Enumerate the resistances to rolling motions. 

77. What are bilge keels, and why are they fitted ? What is the danger 
among waves of great metacentric height ? 

78. What methods may be adopted to obtain steadiness among waves, 
and state clearly the condition of a vessel affected by each of these methods ? 

79. What is meant by synchronism ? How is it produced and how 
averted ? What conditions of loading are most liable to produce it ? 



332 APPENDIX. 

80. State how it is that similar metacentric heights for load and light or 
ballast conditions do not produce similar stability and behaviour at sea. 

81. What are the most important considerations in ballasting as regards 
the amount, position, and securing the ballast? 

82. What is the condition and danger developed by a shifted cargo ? 

83. What means may be adopted to prevent a cargo shifting ? 

84. State under what conditions a vessel's behaviour and stability may 
vary upon a single voyage. 

85. State under what circumstances a ship will sink or capsize, owing 
to the entry of water into the interior, either through an opening in the 
deck or a hole in the side or bottom below the water level. 

86. What are the necessary features or conditions of a vessel in order to 
be able to carry large sail area ? 

87. Enumerate the chief resistances to propulsion, 

CHAPTER VII. 

88. What is meant by the terms "trim," "moment to alter trim," and 
*' moment to alter trim one inch " ? 

89. How would you distribute the cargo in the holds of a vessel so as to 
produce no alteration of trim in immersing her from the light to the load 
draught ? 

90. Explain how you would arrange the cargo in a vessel so as to obtain a 
definite condition of trim. 

91. How is the change of trim estimated, owing to the filling of a fore peak 
tank? 

92. Explain how to estimate the change of trim caused by an empty com- 
partment in the double bottom becoming damaged, and the sea filling the 
compartment. 

93. Give the formula for ** moment to alter trim one inch." 

94. Why is there so great a difference between the height of the longi- 
tudinal metacentre and the vertical metacentre above the centre of buoyancy 
at any particular draught ? 

CHAPTER VIII. 

95. What is meant by gross and under-deck tonnage, and what spaces are 
included in each ? 

96. Enumerate the deductions from the gross tonnage for register tonnage. 

97. How is the propelling space deduction in steamers obtained ? 

98. When are deep water-ballast tanks allowed as deductions, and when 
are they not? 

99. How are deck cargoes reckoned as regards tonnage ? 

100. What are the important differences between the ordinary tonnage 
and Suez Canal tonnage ? 

CHAPTER IX. 

101. What is meant by the term "freeboard '* ? 

102. What are the leading considerations in determining the freeboard for 
any particular vessel ? 

103. Why have spar-decked vessels more freeboard than three-deckers, 
and awning-decked vessels more freeboard than spar-deckers? 

104. What effect have sheer, camber, length, and deck erections upon 
freeboard ? 

APPENDIX A. 

105. Describe Rowe's anti-rolling troughs. 



I1?]"DEX. 



Amidships strength, 60. 
Ardency, 214. 
Atmospheric pressure, 25. 
Awning-deck vessels, 74, 95, 97 ; 
Scantlings of, 102, 103. 



B 



Ballast, Amount and arrangement 
of, 166-185; Means to prevent 
shifting of, 169 ; Minimum ballast 
draught, 180 ; Testing ballast 
tanks, 38 ; Water, 169-185. 

Beam knees, 54. 

Beams, 53, 74, 89 ; Compensation for 
dispensing with, 64; Compensa- 
tion for loss of, in engine and 
boiler space, 76. 

Behaviour, Eft'ect of bilge keels upon, 
150, 163 ; at sea, how affected, 160; 
Alteration of, on a voyage, 161 ; 
how affected by arrangement of 
weights fore and aft, 163 ; how 
affected by arrangement of weights 
transversely, 161 ; how affected by 
metacentric height, 162. 

Bilge, Strengthening of, 53, 56. 
,, keels. Effect of, upon rolling 
motions, 150. 

Boiler stools, 78. 

Bosom piece, 51. 

Breadth, Extreme, 62. 
„ Moulded, 62. 

Breast hook, 89, 90. 

Bridge over half midship length, 76. 

Bridges, Value of, 61. 

Bulb angle, 52, 53. 

Bulkheads, 97-109 ; Height of, 104, 
210 ; liners, 107; longitudinal, 107 ; 
Number of, 97 ; recessed, and means 
of making watertight, 105 ; stiffen- 
ing, 107 ; watertight doors, 108. 



Buoyancy, 19, 113 ; afforded by cargo, 
203 ; Centre of, 23, 27 ; Curves of 
centres of, 28-33 ; effect of camber, 
38 ; Effect of entry of water upon, 
36 ; Effect of longitudinal bulk- 
heads upon, 206 ; Reserve, 22, 26 ; 
Wedges of, 33-36 ; forces among 
waves, 153-160. 

Butts, 51, 58. 

Buttstrap, 109. 



Calculations {see Contents, pages 
271, 301). 

Camber, 38. 

Cargoes, Homogeneous, 188 ; Shift- 
ing, 193. 

Cement washing, 76. 

Centre of effort, 214. 

,, gravity, 14 ; Height of, 
128, 132. 

Centrifugal force, 154. 

Channel bar, 53. 

Coefficients, 10, 11. 

Collars, 107. 

Compensation for dispensing with 
hold beams, 54. 

Connection of longitudinal and trans- 
verse framing, 54-56. 

Cosines, Table of, 268-270. 

Cotangents, Table of, 268-270. 

Countersinking, 110. 

Cylinders, Stability of, 121. 



Deadweight, 6. 

,, scale, 5 ; Relation of, 

to type, 91-97. 
Deck cargoes. Means to support, 91. 

,, erections, Value of, 27. 
Decks, Steel, 75. 



333 



334 



INDEX. 



Deck weights, Means to support, 91. 

Depth, Lloyd's, 62-74 ; moulded, 62 ; 
spar- and awning-deck vessels, 62. 

Diamond plate, 55. 

Displacement, Coefficient of, 10 ; 
curve, Construction of, 3-5 ; De- 
finition of, 1 ; scale, Vertical, 5. 

Double bottom for water ballast, 80, 
170. 

Draught, after lying aground, 25. 
,, Salt and fresh water, 9. 

Drift punch, 109. 



Engine, Foundation plate under, 79 ; 
seat, 76-78 ; space. Strengthening 
of, 76 ; trough, 78. 

Equilibrium, Condition of, 114 ; 
neutral, 115 ; stable, 115 ; un- 
stable, 114. 



Faying surface, 109. 
Flam, 164. 
Flare, 164, 200. 

Floors, 53 ; Dej.th of, 53, 82, 89 ; 
Thickness of, under engines and 
boilers, 76. 
Foot-ton, 12, 112. 
Frame bar, 52. 
,, heel, 61. 
,, spacing, 51. 
Framing, Longitudinal, 40, 57. 

,, Transverse, 40, 51. 
Freeboard, 7 ; Corrections upon, for 
erections on deck, 258 ; for length, 
/ 256 ; for round of beam, 258 ; for 
sheer, 257 ; Definition of, 251 ; 
examples showing how ascertained, 
262-267. 



Garboabd strake, 61. 

Girder, ship. Strengthening flanges 

of, 61. 
Gravity, 14, 113 ; force among waves,* 

154. 
Gunwale, Strengthening of, 61. 



I 



Important terms. Definition of, 

62. 
Intercostal plates, 78, 81. 



K 



Keel, 57-60. 

Keel scarph, 57. 

Keelsons, centre, 58-60 ; Position of, 
60 ; Function of, 60 ; N umber of, 
75 ; compensation for reduced 
depth, 81. 

Kinetic energy, 149. 



H 



Heel piece, 38. 
Hold beams, 74. 



Lateral resistance. Centre of, 213. 

Leeway, 214. 

Length between perpendiculars, 62 ; 
Extreme, 64-73; Lloyd's, 62; 
Standard of, 75, 76. 

Leverage, 12. 

Loading, 186 ; Eflfect of, upon be- 
haviour, 160. 

Lug piece, 69, 60. 



M 



Mast partner, 91. 

Masts, Strengthening and fixing of, 
to resist strain, 91. 

Metacentre, Transverse, 114 ; above 
centre of buoyancy. Rule for, 115 ; 
Curves of, 126, 127 ; Relation of 
design to height of, 118 ; Varia- 
tions in height of, 200. 

Metacentre, Longitudinal, 232 ; Curve 
of, 235. 

Metacentric height. Effect of loading 
upon, 120 ; how found, 128 ; Rela- 
tion of, to wind pressure, 215. 

Metacentric heights, similar. Effect 
of, at different draughts^ 106 ; sta- 
bility, 115. 

Metal chocks, 106. 

Midship sections, 51, 64-72, 80, 
98-102. 

Moments, 12 ; Calculation of, 13-15 ; 
righting and capsizing, 12.